Weighted composition operators on weighted Bergman spaces induced by doubling weights

Abstract

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators uCφ on Bergman type spaces Apω induced by a doubling weight ω. Let X={u∈H(D):uCφ:Apω→Apω is bounded}. For some regular weights ω, we obtain that X=H∞ if and only if ϕ is a finite Blaschke product.