A reproducing kernel thesis for operators on Bergman-type function spaces

TL;DR

This paper investigates the reproducing kernel thesis for boundedness and compactness of operators on Bergman-type spaces, including weighted Bergman and Fock spaces, providing a unified framework for these function spaces.

Contribution

It extends the reproducing kernel thesis to a broad class of Bergman-type spaces and operators, offering new insights into their boundedness and compactness properties.

Findings

Reproducing kernel thesis applies to weighted Bergman spaces

Results encompass operators on the unit ball and polydisc

Framework also covers weighted Fock spaces

Abstract

In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit polydisc and more generally to weighted Fock spaces.