Difference of weighted composition operators on weighted Bergman spaces over the unit Ball

TL;DR

This paper characterizes when differences of weighted composition operators are bounded or compact between weighted Bergman spaces and Lebesgue spaces on the unit ball, extending known results from the unit disk.

Contribution

It provides new criteria for boundedness and compactness of operator differences on weighted Bergman spaces over the unit ball, and introduces a novel characterization of q-Carleson measures.

Findings

Characterization of boundedness of operator differences

Criteria for compactness of operator differences

New description of q-Carleson measures using Bergman metric balls

Abstract

In this paper, we characterize the boundedness and compactness of differences of weighted composition operators from weighted Bergman spaces $A^p_\omega$ induced by a doubling weight $\omega$ to Lebesgue spaces $L^q_\mu$ on the unit ball for full $0<p,q<\infty$, which extend many results on the unit disk. As a byproduct, a new characterization of $q$-Carleson the measure for $A^p_\omega$ in terms of the Bergman metric ball is also presented.