Abstract and Applied Analysis
Volume 2008 (2008), Article ID 605807, 8 pages
doi:10.1155/2008/605807

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.