Essential norms of weighted composition operators from the bergman space to weighted-type spaces on the unit ball

Abstract

We estimate the essential norm of the weighted composition operator uCv from the weighted Bergman space A£(B) to the weighted space ff£(B) on the unit ball B, when p > 1 and oj > -1 (for a = -1, AE is the Hardy space Hp{&)). We also give a necessary and sufficient condition for the operator uCv : Ae(B) -> H™(M) to be compact, and for the operator uCv : Ag(B) -»H™0(B) to be bounded or compact, when p > 0, a > -1.