[[[[[ 研究業績一覧 : List of Publications -- 中井英一 : Eiichi Nakai ]]]]]

[[[[[ 書籍 : books ]]]]]

  1. Editors Akihiko Miyachi, Eiichi Nakai and Masami Okada, Harmonic Analysis and its Applications, 2006, Yokohama Publishers.
    ISBN 4-946552-20-0

  2. 荷見守助 編著，岡裕和，榊原暢久，中井英一 著 (M. Hasumi, H. Oka, N. Sakakibara and E. Nakai), 解析入門 (Introduction to Calculus), (Japanese), 内田老鶴圃 (Uchida R\^okakuho), Tokyo, 1998.
    ISBN 4-7536-0095-5

[[[[[ 論文 : papers ]]]]]

  1. Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai, On the critical Caffarelli-Kohn-Nirenberg type inequalities involving super-logarithms, to appear in Hiroshima Mathematical Journal.

  2. Satoshi Yamaguchi, Eiichi Nakai and Katsunori Shimomura, Bi-predual spaces of generalized Campanato spaces with variable growth condition, Acta Mathematica Sinica, Published online (December 20, 2024). Springer https://doi.org/10.1007/s10114-024-3368-7

  3. 中井英一 (Eiichi Nakai), 多変数フーリエ級数の収束問題とガウスの円問題 (The convergence problem of multiple Fourier series and Gauss's circle problem), 研究紀要 (Research Bulletin), 日本大学経済学部 (Nihon University College of Economics), No. 98 (September 2023), 143--161. 日本大学経済学部研究紀要 第98号 139--157

  4. Fatih Deringoz, Vagif S. Guliyev, Eiichi Nakai, Yoshihiro Sawano and Minglei Shi, Erratum to: Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz-Morrey spaces of the third kind, Positivity 28 (May 2024), article number 42, 6 pp. Springer https://doi.org/10.1007/s11117-023-01023-2

  5. Ryota Kawasumi, Eiichi Nakai and Minglei Shi, Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz-Morrey and weak Orlicz-Morrey spaces, Mathematische Nachrichten, Volume 296, Issue 4 (April 2023), 1483--1503. (Early View. First published: February 8, 2023). Wiley https://doi.org/10.1002/mana.202000332

  6. Kohei Amagai, Eiichi Nakai and Gaku Sadasue, Generalized fractional integral operators based on symmetric Markovian semigroups with application to the Heisenberg group, Taiwanese Journal of Mathematics, Volume 27 (February 2023), No. 1, 113--139. (Advance Publication: September 28, 2022). Project Euclid https://doi.org/10.11650/tjm/220904

  7. Satoshi Yamaguchi and Eiichi Nakai, Compactness of Commutators of Integral Operators with Functions in Campanato Spaces on Orlicz-Morrey Spaces, Journal of Fourier Analysis and Applications, Volume 28 (April 2022), issue 2, Article 33, 32pp. (Published Online: March 23, 2022). Springer https://doi.org/10.1007/s00041-022-09920-y

  8. Mitsuo Izuki, Eiichi Nakai and Yoshihiro Sawano, Atomic and Wavelet Characterization of Musielak-Orlicz Hardy Spaces for Generalized Orlicz Functions, Integral Equations and Operator Theory, Volume 94 (March 2022), issue 1, Article 3, 33 pp. (Published Online: December 17, 2021). Springer https://doi.org/10.1007/s00020-021-02672-2

  9. Shigehiko Kuratsubo and Eiichi Nakai, Multiple Fourier series and lattice point problems, Journal of Functional Analysis, Volume 282, Issue 1 (1 January 2022), Article 109272, 62 pp. ScienceDirect https://doi.org/10.1016/j.jfa.2021.109272

  10. Kazuya Ootsubo, Shoichi Fujima, Shigehiko Kuratsubo and Eiichi Nakai, Kuratsubo phenomenon of the Fourier series of some radial functions in four dimensions, Scientiae Mathematicae Japonicae, Volume 84 (2021) Issue 3, 181--192. J-STAGE DOI https://doi.org/10.32219/isms.84.3_181 (Scientiae Mathematicae Japonicae Online, 2020, e-2020-14, 11 pp. ISMS)

  11. Eiichi Nakai and Yoshihiro Sawano, Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces, Mathematics, Volume 9, Issue 21 (November 1, 2021), Article 2745, 17 pp. MDPI https://doi.org/10.3390/math9212754

  12. Satoshi Yamaguchi and Eiichi Nakai, Generalized fractional integral operators on Campanato spaces and their bi-preduals, Mathematical Journal of Ibaraki University, Volume 53 (2021), 17--34. (Published Online: October 25, 2021.) J-STAGE https://doi.org/10.5036/mjiu.53.17

  13. Katsunori Shimomura and Eiichi Nakai, Biographical sketch of Professor Toshio Horiuchi, Mathematical Journal of Ibaraki University, Volume 53 (2021), i--vii. (Published Online: December 27, 2021.) https://doi.org/10.5036/mjiu.53.i

  14. Ryota Kawasumi and Eiichi Nakai, Weighted boundedness of the Hardy-Littlewood maximal and Calderón-Zygmund operators on Orlicz-Morrey and weak Orlicz-Morrey spaces, Mathematical Inequalities & Applications, Volume 24, Number 4 (October, 2021), 1167--1187. Ele-Math https://doi.org/10.7153/mia-2021-24-81

  15. Victor I. Burenkov, Denny I. Hakim, Eiichi Nakai, Yoshihiro Sawano, Takuya Sobukawa and Tamara V. Tararykova, Complex interpolation of the predual of Morrey spaces over measure spaces, Georgian Mathematical Journal, Volume 28 Issue 3 (June 1, 2021), 341--348. (Published Online: November 26, 2019.) De Gruyter https://doi.org/10.1515/gmj-2019-2070

  16. Ryutaro Arai, Eiichi Nakai and Yoshihiro Sawano, Generalized fractional integral operators on Orlicz-Hardy spaces, Mathematische Nachrichten, Volume 294, Issue 2 (February 2021), 224--235. (published in Early View on November 20, 2020.) Wiley https://doi.org/10.1002/mana.201900052

  17. Minglei Shi, Ryutaro Arai and Eiichi Nakai, Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces, Banach Journal of Mathematical Analysis, Volume 15 (January 2021), issue 1, Article 22, 41pp. (Published Onlien: 23 November 2020) Springer https://doi.org/10.1007/s43037-020-00094-7 arXiv

  18. Ryota Kawasumi and Eiichi Nakai, Pointwise Multipliers on Weak Morrey Spaces, Analysis and Geometry in Metric Spaces, Volume 8 (2020), Issue 1 (Jan 2020), 363--386. (Published online: 31 Dec 2020) DE GRUYTER https://doi.org/10.1515/agms-2020-0119

  19. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Campanato-Morrey spaces for the double phase functionals, Revista Matematica Complutense, Volume 33 (September 2020), Issue 3, 817--834. (Published online: November 25, 2019.) Springer https://doi.org/10.1007/s13163-019-00332-z

  20. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Campanato-Morrey spaces for the double phase functionals with variable exponents, Nonlinear Analysis, Volume 197 (August 2020), 111827. ScienceDirect https://doi.org/10.1016/j.na.2020.111827

  21. Ryutaro Arai, Eiichi Nakai and Gaku Sadasue, Fractional integrals and their commutators on martingale Orlicz spaces, Journal of Mathematical Analysis and Applications, Volume 487, Issue 2 (July 15, 2020), 123991. ScienceDirect https://doi.org/10.1016/j.jmaa.2020.123991

  22. Ryota Kawasumi and Eiichi Nakai, Pointwise multipliers on weak Orlicz spaces, Hiroshima Mathematical Journal, 50 (July 2020), No.2, 169--184. Project Euclid https://doi.org/10.32917/hmj/1595901625 arXivk

  23. Ryutaro Arai and Eiichi Nakai, An extension of the characterization of CMO and its application to compact commutators on Morrey spaces, Journal of the Mathematical Society of Japan, 72 (April, 2020), No. 2, 507--539. (Advance publication: October 28, 2019) Project Euclid https://doi.org/10.2969/jmsj/81458145

  24. Ryutaro Arai and Eiichi Nakai, Compact commutators of Calderón-Zygmund and generalized fractional integral operators with a function in generalized Campanato spaces on generalized Morrey spaces, Tokyo Journal of Mathematics, Volume 42 (December 2019), No. 2, 471--496. (Published online: August 6, 2018) Project Euclid https://doi.org/10.3836/tjm/1502179285

  25. Minglei Shi, Ryutaro Arai and Eiichi Nakai, Generalized fractional integral operators and their commutators with functions in generalized Campanato spaces on Orlicz spaces, Taiwanese Journal of Mathematics, 23 (December 2019), No. 6, 1339--1364. Project Euclid arXivk https://doi.org/10.11650/tjm/181211

  26. Fatih Deringoz, Vagif S. Guliyev, Eiichi Nakai, Yoshihiro Sawano and Minglei Shi, Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz-Morrey spaces of the third kind, Positivity, Volume 23, Issue 3 (July 2019), 727--757. Springer arXivk https://doi.org/10.1007/s11117-018-0635-9

  27. Eiichi Nakai, Generalized Campanato spaces with variable growth condition, Harmonic Analysis and Nonlinear Partial Differential Equations (eds. H. Takaoka, S. Masaki), 65--92, RIMS Kokyuroku Bessatsu B74, Res. Inst. Math. Sci. (RIMS), Kyoto, April, 2019. Kyoto University Research Repository http://hdl.handle.net/2433/244762

  28. Eiichi Nakai and Gaku Sadasue, Commutators of fractional integrals on martingale Morrey spaces. Mathematical Inequalities & Applications, Volume 22, Number 2 (April 2019), 631--655. Ele-Math https://dx.doi.org/10.7153/mia-2019-22-44

  29. Eiichi Nakai and Tsuyoshi Yoneda, Applications of Campanato spaces with variable growth condition to the Navier-Stokes equation, Hokkaido Mathematical Journal, Volume 48, Number 1 (February 2019), 99--140. Project Euclid https://dx.doi.org/10.14492/hokmj/1550480646

  30. Idha Sihwaningrum, Hendra Gunawan and Eiichi Nakai, Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces, Mathematische Nachrichten, Volume 291, Issue 8-9, June 2018, 1400--1417. Wiley https://dx.doi.org/10.1002/mana.201600350

  31. Hendra Gunawan, Denny Ivanal Hakim, Eiichi Nakai and Yoshihiro Sawano, The Hardy and Heisenberg inequalities in Morrey spaces, Bulletin of the Australian Mathematical Society, Volume 97, Issue 3, June 2018, 480--491. (Published online: 28 March, 2018) Cambridge https://doi.org/10.1017/S0004972717001216

  32. Ryutaro Arai and Eiichi Nakai, Commutators of Calderon-Zygmund and generalized fractional integral operators on generalized Morrey spaces, Revista Matematica Complutense, Volume 31, Issue 2 (May 2018), 287--331. (Published online: 23 November, 2017) Springer https://doi.org/10.1007/s13163-017-0251-4

  33. Hendra Gunawan, Denny Ivanal Hakim, Eiichi Nakai and Yoshihiro Sawano, On inclusion relation between weak Morrey spaces and Morrey spaces, Nonlinear Analysis, 168 (March 2018), 27--31. Elsevier https://doi.org/10.1016/j.na.2017.11.005

  34. Wei Li, Eiichi Nakai and Dongyong Yang, Pointwise multipliers on BMO spaces with non-doubling measures, Taiwanese Journal of Mathematics, Volume 22, Number 1 (February 2018), 183--203. (Advance publication: 17 August 2017) Project Euclid https://doi.org/10.11650/tjm/8140

  35. Eiichi Nakai, Pointwise multipliers on Musielak-Orlicz-Morrey spaces, Function spaces and inequalities, 257--281, Springer Proceedings in Mathematics & Statistics 206, Springer, Singapore, 2017. Springer https://doi.org/10.1007/978-981-10-6119-6_13

  36. Eiichi Nakai, Singular and fractional integral operators on preduals of Campanato spaces with variable growth condition, Science China Mathematics, Volume 60, Issue 11, November 2017, 2219--2240. (First Online: 06 September 2017) Springer https://doi.org/10.1007/s11425-017-9154-y

  37. Eiichi Nakai and Gaku Sadasue, Characterizations of boundedness for generalized fractional integrals on martingale Morrey spaces, Mathematical Inequalities & Applications, Volume 20, Number 4, 2017, 929--947. Ele-Math https://doi.org/10.7153/mia-2017-20-58

  38. Eiichi Nakai and Gaku Sadasue, Some new properties concerning BLO martingales, Tohoku Mathematical Journal, Volume 69, Number 2, June 2017, 183--194. Project Euclid https://doi.org/10.2748/tmj/1498269622

  39. Eiichi Nakai, Pointwise multipliers on several function spaces -- a survey --, Linear and Nonlinear Analysis, Volume 3, Number 1, 2017, 27--59. Yokohama Publishers

  40. Eiichi Nakai, Pointwise multipliers on Musielak-Orlicz spaces, Nihonkai Mathematical Journal, Volume 27, Number 1, 2016, 135--146. Project Euclid

  41. Eiichi Nakai and Takuya Sobukawa, \( B_w^u \)-function spaces and their interpolation, Tokyo Journal of Mathematics, Volume 39, Number 2 (2016), 483--516. Project Euclid arXiv DOI: 10.3836/tjm/1459367270

  42. Dachun Yang, Ciqiang Zhuo and Eiichi Nakai, Characterizations of variable exponent Hardy spaces via Riesz transforms, Revista Matematica Complutense, Volume 29, Issue 2, May 2016, 245--270. (First online: 25 January 2016) Springer DOI 10.1007/s13163-016-0188-z

  43. Denny Ivanal Hakim, Eiichi Nakai and Yoshihiro Sawano, Generalized fractional maximal operators and vector-valued inequalities on generalized Orlicz-Morrey spaces Revista Matematica Complutense, Volume 29, Issue 1, January 2016, 59--90. (First online: 08 August 2015) Springer DOI 10.1007/s13163-015-0178-6

  44. Mitsuo Izuki, Eiichi Nakai and Yoshihiro Sawano, Wavelet characterization and modular inequalities for weighted Lebesgue spaces with variable exponent, Annales Academiæ Scientiarum Fennicæ Mathematica. 40 (2015), 551--571. Open Access DOI:10.5186/aasfm.2015.4032

  45. Mitsuo Izuki, Eiichi Nakai and Yoshihiro Sawano, Function spaces with variable exponents -- an introduction --, Scientiae Mathematicae Japonicae, Volume 77, No. 2 (2014 August), 187--315. J=STAGE DOI: https://doi.org/10.32219/isms.77.2_187 (Scientiae Mathematicae Japonicae Online, e-2014, 153--281. Online)

  46. Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai, Some properties of slowly increasing functions, Mathematical Journal of Ibaraki University, Volume 46 (2014 July), 37--49. J-STAGE DOI: https://doi.org/10.5036/mjiu.46.37

  47. Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai, Weighted Hardy inequalities with infinitely many sharp missing terms, Mathematical Journal of Ibaraki University, Volume 46 (2014 July), 9--30. J-STAGE DOI: https://doi.org/10.5036/mjiu.46.9

  48. Eiichi Nakai and Yoshihiro Sawano, Orlicz-Hardy spaces and their duals, Science China Mathematics, Volume 57, Number 5 (2014 May), 903--962. Springer DOI:10.1007/s11425-014-4798-y

  49. Eridani, Hendra Gunawan, Eiichi Nakai and Yoshihiro Sawano, Characterizations for the generalized fractional integral operators on Morrey spaces, Mathematical Inequalities & Applications Volume 17, Number 2 (2014 April), 761--777. Ele-Math DOI:10.7153/mia-17-56

  50. Eiichi Nakai and Gaku Sadasue, Pointwise multipliers on martingale Campanato spaces, Studia Mathematica, Volume 220, Number 1 (2014), 87--100. Studia Mathematica arXiv DOI:10.4064/sm220-1-5

  51. Eiichi Nakai, Generalized fractional integrals on generalized Morrey spaces, Mathematische Nachrichten, Volume 287, Number 2-3 (2014 February), 339-351. Wiley Online Library DOI:10.1002/mana.201200334

  52. Yiyu Liang, Eiichi Nakai, Dachun Yang and Junqiang Zhang, Boundedness of intrinsic Littlewood-Paley functions on Musielak-Orlicz Morrey and Campanato Spaces, Banach Journal of Mathematical Analysis, Volume 8, Number 1 (2014 January), 221--268. Open Access arXiv DOI:10.15352/bjma/1381782098

  53. Eiichi Nakai, Gaku Sadasue and Yoshihiro Sawano, Martingale Morrey-Hardy and Campanato-Hardy Spaces, Journal of Function Spaces and Applications, Volume 2013 (20 October 2013), Article ID 690258, 14 pages Open Access DOI:10.1155/2013/690258

  54. Eiichi Nakai and Gaku Sadasue, Maximal function on generalized martingale Lebesgue spaces with variable exponent, Statistics & Probability Letters, Volume 83, Issue 10 (October 2013), 2168--2171. ScienceDirect DOI:10.1016/j.spl.2013.06.007

  55. Mitsuo Izuki, Eiichi Nakai and Yoshihiro Sawano, Hardy spaces with variable exponent, Harmonic analysis and nonlinear partial differential equations, 109--136, RIMS Kokyuroku Bessatsu B42, Res. Inst. Math. Sci. (RIMS), Kyoto, August, 2013.

  56. Mitsuo Izuki, Eiichi Nakai and Yoshihiro Sawano, The Hardy-Littlewood maximal operator on Lebesgue spaces with variable exponent, Harmonic analysis and nonlinear partial differential equations, 51--94, RIMS Kokyuroku Bessatsu B42, Res. Inst. Math. Sci. (RIMS), Kyoto, August, 2013.

  57. Yoshihiro Mizuta, Eiichi Nakai, Yoshihiro Sawano and Tetsu Shimomura, Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials, Journal of the Mathematical Society of Japan, Volume 65, Number 2 (April 2013), 633--670. Project Euclid DOI:10.2969/jmsj/06520633

  58. Yasuo Komori-Furuya, Katsuo Matsuoka, Eiichi Nakai and Yoshihiro Sawano, Applications of Littlewood-Paley theory for \( B_{\sigma} \)-Morrey spaces to the boundedness of integral operators, Journal of Function Spaces and Applications, Volume 2013 (13 March 2013), Article ID 859402, 21 pages. Open Access DOI:10.1155/2013/859402

  59. Yasuo Komori-Furuya, Katsuo Matsuoka, Eiichi Nakai and Yoshihiro Sawano, Integral operators on \( B_{\sigma} \)-Morrey-Campanato spaces, Revista Matematica Complutense, Volume 26, Issue 1 (2013 January), 1--32 SpringerLink Open Access DOI:10.1007/s13163-011-0091-6

  60. Hendra Gunawan, Eiichi Nakai, Yoshihiro Sawano and Hitoshi Tanaka, Generalized Stummel class and Morrey spaces, Publications de l'Institut Mathematique, Volume 92 (2012), 127--138. Open Access DOI:10.2298/PIM1206127G

  61. Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai, Construction of slowly increasing functions, Scientiae Mathematicae Japonicae, Volume 75, No. 2 (August 2012), 187--201. J-STAGE DOI: https://doi.org/10.32219/isms.75.2_187 (Scientiae Mathematicae Japonicae Online, e-2012, 207--221. Online)

  62. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in \( \mathrm{R}^n \), Revista Matematica Complutense, Volume 25, Number 2 (2012), 413--434. SpringerLink DOI:10.1007/s13163-011-0074-7

  63. Eiichi Nakai and Gaku Sadasue, Martingale Morrey-Campanato spaces and fractional integrals, Journal of Function Spaces and Applications, Volume 2012 (09 July 2012), Article ID 673929, 29 pages Open Access DOI:10.1155/2012/673929

  64. Eiichi Nakai and Yoshihiro Sawano, Hardy spaces with variable exponents and generalized Campanato spaces, Journal of Functional Analysis Volume 262, Issue 9 (1 May 2012), 3665--3748. ScienceDirect DOI:10.1016/j.jfa.2012.01.004

  65. Eiichi Nakai and Tsuyoshi Yoneda, Bilinear estimates in dyadic BMO and the Navier-Stokes equations, Journal of the Mathematical Society of Japan, Volume 64, Number 2 (April 2012), 399--422. Project Euclid doi: 10.2969/jmsj/06420399

  66. Takashi Miyamoto, Eiichi Nakai and Gaku Sadasue, Martingale Orlicz-Hardy spaces, Mathematische Nachrichten, Volume 285, Issue 5-6 (April 2012), 670--686. Wiley Online Library DOI:10.1002/mana.201000109

  67. Yoshihiro Mizuta, Eiichi Nakai, Yoshihiro Sawano and Tetsu Shimomura, Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces, Archiv der Mathematik, Volume 98, Number 3 (March 2012), 253-263. SpringerLink DOI:10.1007/s00013-012-0362-6

  68. Katsuo Matsuoka and Eiichi Nakai, Fractional integral operators on \( B^{p,\lambda} \) with Morrey-Campanato norms, Function Spaces IX (Krakow, Poland, 2009), 249--264, Banach Center Publications , Vol.92, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2011. Banach Center Publications DOI:10.4064/bc92-0-17

  69. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Sobolev's inequality for Riesz potentials in Orlicz-Musielak spaces of variable exponent, Banach and Function Spaces III (Kitakyushu, 2009), 409--419, Yokohama Publishers, Yokohama, 2011.

  70. Eiichi Nakai, Orlicz-Morrey spaces and their preduals, Banach and Function Spaces III (Kitakyushu, 2009), 187--205, Yokohama Publishers, Yokohama, 2011.

  71. Haibo Lin, Eiichi Nakai and Dachun Yang, Boundedness of Lusin-area and \( g_{\lambda}^* \) functions on localized Morrey-Campanato spaces over doubling metric measure spaces, Journal of Function Spaces and Applications, Volume 9 (2011), Issue 3, 245--282. Open Access DOI:10.1155/2011/187597

  72. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponent, Complex Variables and Elliptic Equations, Vol.56, Issue 7-9 (July 2011), 671--695. Taylor and Francis Online DOI:10.1080/17476933.2010.504837

  73. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Hardy's inequality in Orlicz-Sobolev spaces of variable exponent, Hokkaido Mathematical Journal, Vol.40, No.2 (June 2011), 187--203.

  74. Eiichi Nakai and Tsuyoshi Yoneda, Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations, Hokkaido Mathematical Journal, Vol.40, No.1 (February 2011), 67--88. Open Access

  75. Haibo Lin, Eiichi Nakai and Dachun Yang, Boundedness of Lusin-area and \( g_{\lambda}^* \) functions on localized BMO spaces over doubling metric measure spaces, Bulletin des Sciences Mathematiques, Vol.135, No.1 (January-February 2011), 59--88. ScienceDirect DOI:10.1016/j.bulsci.2010.03.004 arXiv

  76. Lech Maligranda and Eiichi Nakai, Pointwise multipliers of Orlicz spaces, Archiv der Mathematik, Vol.95, No.3 (September, 2010), 251--256. SpringerLink DOI:10.1007/s00013-010-0160-y

  77. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials, Journal of the Mathematical Society of Japan, Vol.62, No.3 (July, 2010), 707--744. Project Euclid DOI:10.2969/jmsj/06230707

  78. Eiichi Nakai, Singular and fractional integral operators on Campanato spaces with variable growth conditions, Revista Matematica Complutense, Vol.23, No.2 (July, 2010) 355--381. SpringerLink DOI:10.1007/s13163-009-0022-y

  79. Shigehiko Kuratsubo, Eiichi Nakai and Kazuya Ootsubo, Generalized Hardy identity and relations to Gibbs-Wilbraham and Pinsky phenomena, Journal of Functional Analysis, Vol.259 (July, 2010), 315--342. ScienceDirect (Open Archive) DOI:10.1016/j.jfa.2010.03.025

  80. Yan Meng, Eiichi Nakai and Dachun Yang, Estimates for Lusin-area and Littlewood-Paley \( g^*_{\lambda} \) functions over spaces of homogeneous type, Nonlinear Anal., Vol.72, No.5 (March, 2010), 2721--2736. ScienceDirect DOI:10.1016/j.na.2009.11.019

  81. Eiichi Nakai and Tsuyoshi Yoneda, Construction of solutions for the initial value problem of a functional-differential equation of advanced type, Aequationes Mathematicae, Vol.77, No. 3 (June, 2009), 259-272. SpringerLink DOI:10.1007/s00010-009-2965-y

  82. Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura, An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces \( L^{1,\nu,\beta}(G) \), Hiroshima Mathematical Journal, Vol.38 (2008), 425-436. Project Euclid

  83. Eiichi Nakai, A generalization of Hardy spaces \( H^p \) by using atoms, Acta Mathematica Sinica, Vol.24 (2008), 1243--1268. SpringerLink DOI:10.1007/s10114-008-7626-x

  84. Eiichi Nakai, Orlicz-Morrey spaces and the Hardy-Littlewood maximal function, Studia Mathematica, Vol.188, No.3 (2008), 193--221. Studia Mathematica DOI:10.4064/sm188-3-1

  85. Eiichi Nakai, Calderón-Zygmund operators on Orlicz-Morrey spaces and modular inequalities, Banach and Function Spaces II (Kitakyushu, 2006), 393--410, Yokohama Publishers, Yokohama, 2008.

  86. Eiichi Nakai, Recent topics of fractional integrals, Sugaku Expositions, American Mathematical Society, Vol.20, No.2 (2007), 215--235. Osaka Kyoiku University Repository

  87. Norio Kikuchi, Eiichi Nakai, Naohito Tomita, Kôzô Yabuta and Tsuyoshi Yoneda, Calderón-Zygmund operators on amalgam spaces and in the discrete case, Journal of Mathematical Analysis and Applications, Vol.335 (2007), 198--212. ScienceDirect DOI:10.1016/j.jmaa.2007.01.043

  88. Eiichi Nakai, The Campanato, Morrey and Hölder spaces on spaces of homogeneous type, Studia Mathematica, Vol.176, No.1 (2006), 1--19. Studia Mathematica DOI:10.4064/sm176-1-1

  89. Shigehiko Kuratsubo, Eiichi Nakai and Kazuya Ootsubo, On the Pinsky Phenomenon of Fourier Series of the Indicator Function in Several Variables, Memoirs of Osaka Kyoiku University, Ser.III Natural Science and Applied Science Vol.55, No.1 (2006), 1--20. Osaka Kyoiku University Repository

  90. Eiichi Nakai, Construction of an atomic decomposition for functions with compact support, Journal of Mathematical Analysis and Applications, Vol.313 (2006), 730--737. ScienceDirect DOI:10.1016/j.jmaa.2005.07.072

  91. Eiichi Nakai, Generalized fractional integrals on Orlicz-Morrey spaces, Banach and Function Spaces (Kitakyushu, 2003), 323--333, Yokohama Publishers, Yokohama, 2004.

  92. 中井英一 (Eiichi Nakai), Fractional integral の最近の話題 (Recent topics of fractional integrals), 数学 第56巻 (2004), 260--280 (Sugaku Vol.56 (2004), 260--280). Journal@rchive Osaka Kyoiku University Repository

  93. Eridani, Hendra Gunawan and Eiichi Nakai, On generalized fractional integral operators, Scientiae Mathematicae Japonicae, Volume 60, No. 3 (November 2004), 539--550. (Scientiae Mathematicae Japonicae Online, Vol.10 (2004), 307--318. Online)

  94. Eiichi Nakai, Naohito Tomita and Kôzô Yabuta, Density of the set of all infinitely differentiable functions with compact support in weighted Sobolev spaces, Scientiae Mathematicae Japonicae, Volume 60, No. 1 (July 2004), 121--127. (Scientiae Mathematicae Japonicae Online, Vol.10 (2004), 39--45. Online)

  95. Eiichi Nakai and Shigeo Okamoto, Tangential boundary behavior of the Poisson integrals of functions in the potential space with the Orlicz norm, Scientiae Mathematicae Japonicae, Volume 59, No. 3 (May 2004), 407--428. (Scientiae Mathematicae Japonicae Online, Vol.9 (2003), 187--208. Online)

  96. Eiichi Nakai, On generalized fractional integrals on the weak Orlicz spaces, \( \mathrm{BMO}_{\phi} \), the Morrey spaces and the Campanato spaces, Function spaces, interpolation theory and related topics (Lund, 2000), 389--401, Walter de Gruyter, Berlin, New York, 2002. De Gruyter DOI:10.1515/9783110198058.389 eBook ISBN: 9783110198058

  97. Chikako Harada and Eiichi Nakai, The square partial sums of the Fourier transform of radial functions in three dimensions, Scientiae Mathematicae Japonicae, Volume 55, No. 3 (May 2002), 467--477. (Scientiae Mathematicae Japonicae Online, Vol.5 (2001), 329--339. Online)

  98. Eiichi Nakai, On generalized fractional integrals, Taiwanese Journal of Mathematics, Vol.5 (September 2001), 587--602. Project Euclid DOI: 10.11650/twjm/1500574952

  99. Eiichi Nakai, On generalized fractional integrals in the Orlicz spaces on spaces of homogeneous type, Scientiae Mathematicae Japonicae, Volume 54, No. 3 (November 2001), 473--487. (Scientiae Mathematicae Japonicae Online, Vol.4 (2001), 901--915. Online)

  100. Eiichi Nakai and Hironori Sumitomo, On generalized Riesz potentials and spaces of some smooth functions, Scientiae Mathematicae Japonicae, Volume 54, No. 3 (November 2001), 463--472. (Scientiae Mathematicae Japonicae Online, Vol.4 (2001), 891--900. Online)

  101. Eiichi Nakai, A characterization of pointwise multipliers on the Morrey spaces, Scientiae Mathematicae, Vol.3 (2000), 445--454. Online)

  102. Eiichi Nakai, On generalized fractional integrals in the Orlicz spaces, Proceedings of the Second ISAAC Congress, Kluwer Academic Publishers B. V. Netherland-U. S. A., 2000, 75--81. Springer https://doi.org/10.1007/978-1-4613-0269-8

  103. Eiichi Nakai, Pointwise multipliers on the Morrey Spaces, Memoirs of Osaka Kyoiku University, Ser.III Natural Science and Applied Science Vol.46 (1997), no. 1, 1--11. Osaka Kyoiku University Repository

  104. Eiichi Nakai, Pointwise multipliers on weighted BMO spaces, Studia Mathematica, Vol.125, No.1 (1997), 35--56. Studia Mathematica DOI: 10.4064/sm-125-1-35-56

  105. Eiichi Nakai and Kôzô Yabuta, Pointwise multipliers for functions of weighted bounded mean oscillation on spaces of homogeneous type, Mathematica Japonica, Vol.46 (1997), 15--28.

  106. Eiichi Nakai, Pointwise multipliers on the Lorentz Spaces, Memoirs of Osaka Kyoiku University, Ser.III Natural Science and Applied Science Vol.45 (1996), no. 1, 1--7. Osaka Kyoiku University Repository

  107. Eiichi Nakai, Pointwise multipliers, Memoirs of The Akashi College of Technology, Vol.37 (1995), 85--94.

  108. Eiichi Nakai, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Mathematische Nachrichten, Volume 166 (1994), Issue 1, 95--103. InterScience DOI:10.1002/mana.19941660108

  109. Eiichi Nakai, Pointwise multipliers for functions of weighted bounded mean oscillation, Studia Mathematica, Vol.105, No.2 (1993), 105--119. Studia Mathematica DOI: 10.4064/sm-105-2-105-119

  110. Eiichi Nakai and Kôzô Yabuta, Singular integral operators on \( L^{p,\Phi} \)-spaces, Annali di Matematica pura ed applicata, Vol.153 (1988), 53--62. SpringerLink DOI: https://doi.org/10.1007/BF01762385

  111. Eiichi Nakai, Singular integral operators on \( L_k^{p,\Phi} \)-spaces, Bulletin of the Faculty of Science, Ibaraki University, Series A. Mathematics, Vol.19 (1987), 71--78. J-STAGE DOI: https://doi.org/10.5036/bfsiu1968.19.71

  112. Eiichi Nakai and Kôzô Yabuta, Pointwise multipliers for functions of bounded mean oscillation, Journal of the Mathematical Society of Japan, Vol.37, No.2 (April 1985), 207--218. Project Euclid DOI:10.2969/jmsj/03720207

  113. Eiichi Nakai, On the restriction of functions of bounded mean oscillation to the lower dimensional space, Archiv der Mathematik, Vol.43 (1984), 519--529. SpringerLink DOI: https://doi.org/10.1007/BF01190955

[[[[[ 数理解析研究所講究録：RIMS Kôkyûroku ]]]]]

  1. 中井英一(Eiichi Nakai), Pointwise multipliers and generalized Campanato spaces with variable growth condition, 関数空間論とその周辺 (Theory of function spaces and related topics), 京都大学 数理解析研究所講究録 2250 (2023年5月), 195--235 (RIMS Kôkyûroku No. 2250 (May, 2023), 195--235). Kyoto University Research Information Repository

  2. 中井英一(Eiichi Nakai), 貞末岳(Gaku Sadasue), Fractional integrals on martingale spaces, 関数空間の構造とその周辺 (The structure of function spaces and its environment), 京都大学 数理解析研究所講究録 2041 (2017年7月), 220--226 (RIMS Kôkyûroku No. 2041 (July, 2017), 220--226). Kyoto University Research Information Repository

  3. 中井英一 (Eiichi Nakai), Pointwise multipliers on Musielak-Orlicz and Musielak-Orlicz-Morrey spaces, 等距離写像研究の多角的アプローチ (Researches on isometries from various viewpoints), 京都大学 数理解析研究所講究録 2035 (2017年7月), 80--93 (RIMS Kôkyûroku No. 2035 (July, 2017), 80--93). Kyoto University Research Information Repository

  4. 松岡勝男 (Katsuo Matsuoka), 中井英一 (Eiichi Nakai), Singular integral operators and \( B^{p,\lambda} \) with Morrey-Campanato norms, バナッハ空間論の研究とその周辺 (Banach space theory and related topics), 京都大学 数理解析研究所講究録 1753 (2011年8月), 67--76 (RIMS Kôkyûroku No. 1753 (August, 2011), 67--76). Kyoto University Research Information Repository

  5. 中井英一 (Eiichi Nakai), 貞末岳 (Gaku Sadasue), Martingale Morrey-Campanato spaces, バナッハ空間論の研究とその周辺 (Banach space theory and related topics), 京都大学 数理解析研究所講究録 1753 (2011年8月), 58--66 (RIMS Kôkyûroku No. 1753 (August, 2011), 58--66). Kyoto University Research Information Repository

  6. 中井英一 (Eiichi Nakai), Predual of Campanato spaces and Riesz potentials, ポテンシャル論とその関連分野 (Potential Theory and its related Fields), 京都大学 数理解析研究所講究録 1669 (2009年11月), 122--131 (RIMS Kôkyûroku No. 1669 (November, 2009), 122--131). Kyoto University Research Information Repository

  7. Eiichi Nakai and Tsuyoshi Yoneda, Convergence of some truncated Riesz transforms on predual of generalized Campanato spaces and its application to a uniqueness theorem for nondecaying solutions of Navier-Stokes equations. The geometrical structure of Banach spaces and Function spaces and its applications (Japanese), 京都大学 数理解析研究所講究録 1667 (2009年11月) 71--79 (RIMS Kôkyûroku No. 1667 (November, 2009), 71--79). Kyoto University Research Information Repository

  8. Eiichi Nakai, A generalization of Hardy spaces on spaces of homogeneous type, Recent results of Banach and function spaces and its applications (Japanese), RIMS Kôkyûroku No. 1615 (October, 2008), 99--106. Kyoto University Research Information Repository

  9. Eiichi Nakai, Preduals of Morrey-Campanato spaces, Banach spaces, function spaces, inequalities and their applications (Japanese), RIMS Kôkyûroku No. 1570 (2007), 46--53. Kyoto University Research Information Repository

  10. Eiichi Nakai, On Orlicz-Morrey spaces, The structure of Banach spaces and Function spaces (Japanese), RIMS Kôkyûroku No. 1520 (2006), 78--88. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  11. Eiichi Nakai, Naohito Tomita and Kôzô Yabuta, Fourier multipliers and decomposition of functions by convolution, Communication in commutative Banach algebras and several field of mathematics (Japanese), RIMS Kôkyûroku No. 1478 (2006), 116--126. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  12. Eiichi Nakai, Naohito Tomita and Kôzô Yabuta and Tsuyoshi Yoneda, Boundedness of singular integral operators on some Morrey and amalgam spaces (Japanese), Banach and function spaces and their application (Japanese), RIMS Kôkyûroku No. 1455 (2005), 128--136. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  13. Eiichi Nakai, Naohito Tomita and Kôzô Yabuta, Extensions of Fig`a-Talamanca's multiplier theorem to Banach function spaces, Banach and function spaces and their application (Japanese), RIMS Kôkyûroku No. 1455 (2005), 1--7. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  14. Eiichi Nakai, Orlicz-Morrey spaces and some integral operators, The structure of Banach spaces and its application (Japanese) RIMS Kôkyûroku No. 1399 (2004), 144--156. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  15. Eiichi Nakai, Hardy spaces and generalized fractional integrals, Harmonic Analysis and Nonlinear Partial Differential Equations, RIMS Kôkyûroku No. 1388 (2004), 1--22. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  16. Eiichi Nakai, Hardy spaces and preduals of Campanato spaces (Japanese), Harmonic/analytic function spaces and linear operators, II (Japanese), RIMS Kôkyûroku No. 1277, (2002), 67--77. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  17. Eiichi Nakai, Generalized fractional integrals, RIMS Kôkyûroku No. 1201 (2001), 56--74. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  18. Eiichi Nakai, On generalized fractional integrals, RIMS Kôkyûroku No. 1137, (2000), 61--70. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  19. Eiichi Nakai, Pointwise multipliers on Campanato spaces and Morrey spaces (Japanese), Harmonic/analytic function spaces and linear operators (Japanese) (Kyoto, 1998), RIMS Kôkyûroku No. 1049 , (1998), 1--10. 46E30 (46M35). Kyoto University Research Information Repository Osaka Kyoiku University Repository

  20. Eiichi Nakai, Weighted BMO on homogeneous spaces (Japanese), The structure of spaces of analytic and harmonic functions and the theory of operators on them (Japanese) (Kyoto, 1995), RIMS Kôkyûroku No. 946 , (1996), 141--151. 42B15. Kyoto University Research Information Repository Osaka Kyoiku University Repository

  21. Eiichi Nakai and Kôzô Yabuta, Pointwise multipliers on \( \mathrm{bmo}_{\phi}(\mathbb{R}^n) \) (Japanese), RIMS Kôkyûroku No. 523 (1984), 192--207. Kyoto University Research Information Repository

[[[[[ 数学セミナー : Sugaku Seminar ]]]]]

  1. 中井英一 (Eiichi Nakai), 超関数とフーリエ変換 (Distributions and the Fourier transform), 数学セミナー, 2018年3月号, 通巻 677号, 28--33 (Sugaku Seminar, 677 (March, 2018), 28--33). Nippon Hyoron sha co.,Ltd.

  2. 中井英一 (Eiichi Nakai), ヒルベルト空間上の完全連続な自己共役作用素 (Completely continuous self-adjoint operators on Hirbert spaces), 数学セミナー 2012年12月号 通巻 614号, 34--41 (Sugaku Seminar, 614 (December, 2012), 34--41). Nippon Hyoron sha co.,Ltd.

  3. 中井英一 (Eiichi Nakai), フーリエ級数の収束問題／多変数フーリエ級数の特異現象 (The convergence problem of Fourier series -- singular phenomena of multi-dimensional Fourier series --), 数学セミナー 2010年10月号 通巻 589号, 31--37 (Sugaku Seminar, 589 (October, 2010), 31--37). Nippon Hyoron sha co.,Ltd.

[[[[[ その他の著作 (1) : Others (1) ]]]]]

  1. 中井英一, 書評「北廣男著、オーリッチ空間とその応用、岩波書店、2009/12」, 国際数理科学協会会報, No. 81 (2012.5), 5--6. 国際数理科学協会

  2. Kazuya Ootsubo, Shigehiko Kuratsubo, Eiichi Nakai and Akihiro Hayami, Voronoi-Hardy's identity, the Gibbs-Wilbraham phenomenon, the Pinsky phenomenon and the third phenomenon, Presentation at MSJ Autumn Meeting 2009, 12 pp. Osaka Kyoiku University Repository

[[[[[ その他の著作 (2) : Others (2) ]]]]]
  1. 中井英一, TeX の紹介, 大阪教育大学情報処理センター年報, 第7号 (2004), 1--4.

  2. 中井英一, プログラム言語の性格を持つワープロソフト TeX --- 数学教育専攻学生向け「総合演習」の報告 ---, 数学教育研究 (Osaka Journal of Mathematics Education) 大阪教育大学数学教室, 第33号 (2003), 149--159.

[[[[[ 口頭発表 : Talks ]]]]]

List of Talks

[[[[[ 2022年度日本数学会解析学賞：prize ]]]]]

[[[[[ 科学研究費補助金 研究成果トピックス ]]]]]

[[[[[ 科学研究費補助金（研究代表者） : Grants-in-aid ]]]]]
2014/2/17, 2022/3/27
Eiichi Nakai, Ibaraki University

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