Weighted composition operators on weighted Bergman spaces of bounded symmetric domains

TL;DR

This paper investigates the boundedness, compactness, and Schatten class membership of weighted composition operators on weighted Bergman spaces of bounded symmetric domains using Carleson measure techniques.

Contribution

It provides necessary and sufficient conditions for boundedness and compactness of weighted composition operators and explores their Schatten p-class properties.

Findings

Characterized boundedness and compactness criteria for weighted composition operators.

Established conditions for Schatten p-class membership.

Applied Carleson measure techniques to analyze operator properties.

Abstract

In this paper, we study the weighted compositon operators on weighted Bergman spaces of bounded symmetric domains. The necessary and sufficient conditions for a weighted composition operator $W_{\phi,\psi}$ to be bounded and compact are studied by using the Carleson measure techniques. In the last section, we study the Schatten p-class weighted composition operators.