Bounded operators on the weighted spaces of holomorphic functions on the unit ball in $C^n$

Abstract

Assuming that $S$ is the space of functions of regular variation, $\omega \in S$, $0<p<\infty$, a function $f$ holomorphic in $B^n$ is said to be of Besov space $B_p(\omega )$ if $$\Vert f{\Vert }_{B_p(\omega )}^p={\int }_{B^n}(1-|z{|}^2{)}^p|Df(z){|}^p\frac{\omega (1-|z|)}{(1-|z{|}^2{)}^{n+1}}d\nu (z)<+\infty ,$$ where $d\nu (z)$ is the volume measure on $B^n$ and $D$ stands for a fractional derivative of $f$. We consider operators on $B_p(\omega )$ and show, that they are bounded.

13 pages