Quasiconformally invariant function spaces
Pekka Koskela
Abstract:
It is almost immediate from the definition that the homogeneous Sobolev space
consisting of functions with n-integrable gradients is invariant under
quasiconformal
mappings of an n-dimensional Euclidean space when n is at least two.
This invariance actually characterizes quasiconformality. Reimann proved that
also BMO is invariant. By interpolation, one concludes that also the diagonal
Besov spaces with 0~~n/(n+s), but the case of Besov spaces was left open. I
will explain this result and
the even more recent result (Koch-Koskela-Saksman-Soto) for the Besov scales.
~~