Difference of composition operators on weight Bergman spaces with doubling weight

TL;DR

This paper characterizes when the difference of composition operators is compact on weighted Bergman spaces with doubling weights, extending previous results to a broader class of weights.

Contribution

It provides new characterizations for the compactness of the difference of composition operators on weighted Bergman spaces with doubling weights, generalizing Moorhouse's work.

Findings

Characterizations for compact difference of composition operators

Extension of Moorhouse's characterization to doubling weights

Broader understanding of operator behavior on weighted spaces

Abstract

In this paper, some characterizations for the compact difference of composition operators on Bergman spaces $A^p_\omega$ with doubling weight are given, which extend Moorhouse's characterization for the difference of composition operators on the weighted Bergman space $A^2_\alpha$.