Characterizations for the difference of weighted composition operators over the polydisk

Abstract

In this paper, we have established the characterizations for the boundedness and compactness of the difference of weighted composition operators acting on the weighted Bergman spaces over the polydisk when weight functions are Lebesgue integrable. In particular, our results contain the Reproducing kernel thesis for the difference of weighted composition operators. As an application, we obtain a function-theoretic characterization when the weight functions are holomorphic and essentially bounded. © 2023 Elsevier Inc.