Bounded operators on weighted spaces of holomorphic functions on the polydisk

TL;DR

This paper investigates the boundedness of various operators, including Toeplitz, Hankel, and Berezin-type, on weighted spaces of holomorphic functions on the polydisk, expanding understanding of operator behavior in these function spaces.

Contribution

It establishes new boundedness theorems for Toeplitz, Hankel, and Berezin-type operators on weighted holomorphic function spaces on the polydisk.

Findings

Boundedness of Toeplitz operators on weighted Besov spaces

Boundedness of generalized Hankel operators on weighted spaces

Boundedness of Berezin-type operators on weighted spaces

Abstract

We consider the weighted $A^p(\omega)$ and $B_p(\omega)$ spaces of holomorphic functions on the polydisk (in the case of $p>1$). We prove some theorems about the boundedness of Toeplitz operators on weighted Besov spaces $B_p(\omega)$ and about the boundedness of generalized little Hankel and Berezin- type operators on $A^p(\omega)$.