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 $$\|f\|^p_{B_p(\omega )}=\int_{B^n} (1-|z|^2)^p|Df(z)|^p\frac{\omega(1-|z|)}{(1-|z|^2)^{n+1}}d\nu(z) <+\infty,$$ 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.