Weighted Composition Operators on Some Weighted Spaces in the Unit Ball

Abstract

Let Bn be the unit ball of Cn, H(Bn) the space of all holomorphic functions in Bn. Let u∈H(Bn) and α be a holomorphic self-map of Bn. For f∈H(Bn), the weigthed composition operator uCα is defined by (uCαf)(z)=u(z)f(α(z)),z∈Bn. The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.