A characterization for the boundedness of positive operators in a filtered measure space

Hitoshi Tanaka 

Abstract:
In terms of Sawyer type checking condition,
a complete characterization is established
for which in a filtered measure space
the positive operator is bounded from $L^p(d\mu)$ to $L^q(d\mu)$
with $1<p\le q<\infty$.
This is a joint work with Dr. Yutaka Terasawa.