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 $A^p_\omega$ 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.