The weighted composition operators on the large weighted Bergman spaces

TL;DR

This paper characterizes various properties of weighted composition operators on large weighted Bergman spaces with exponential weights, extending previous results and providing new criteria for boundedness and compactness.

Contribution

It offers a comprehensive characterization of bounded, compact, and Schatten class weighted composition operators on large weighted Bergman spaces, including a proof of a necessary condition from prior work.

Findings

Characterization of bounded, compact, and Schatten class operators

Extension of boundedness criteria to large weighted Bergman spaces

Proof of necessary conditions for boundedness from previous studies

Abstract

In this paper, we characterize bounded, compact or Schatten class weighted composition operators acting on Bergman spaces with the exponential type weights. Moreover, we give the proof of the necessary part for the boundedness of composition operators on large weighted Bergman spaces given by Kriete and Maccluer in 1992.