Essential norm and Schatten class difference of weighted composition operators over the ball

TL;DR

This paper estimates the essential norm of differences of weighted composition operators on weighted Bergman spaces over the unit ball and characterizes when these differences belong to Schatten classes, using Carleson measures and R-Berezin transforms.

Contribution

It provides new estimates for the essential norm and characterizations of Schatten class membership for differences of weighted composition operators.

Findings

Essential norm estimates for operator differences

Characterizations of Schatten class membership

Application of Carleson measures and R-Berezin transform

Abstract

In this paper, we obtain the essential norm estimate for the difference of two weighted composition operators acting on standard weighted Bergman spaces over the unit ball. And we get some characterizations for the difference of weighted composition operators belonging to Schatten class, which has rarely been considered before. Our methods are fundamental, which involve Carleson measures and $R$-Berezin transform.