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

Abstract

In this paper, we characterize the boundedness and compactness of differences of weighted composition operators from weighted Bergman spaces $A_{\ddot{I}}^p‰$ induced by a doubling weight $\ddot{I}‰$ to Lebesgue spaces $L_{\hat{I}}^q¼$ 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 $A_{\ddot{I}}^p‰$ in terms of the Bergman metric ball is also presented.