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

Weighted Composition Operators on Some Weighted Spaces in the Unit Ball

Xiaohong Fu and Xiangling Zhu

 Department of Mathematics, Jiaying University Guangdong, Meizhou 514015, China
Received 18 May 2008; Accepted 28 May 2008

Recommended by Stevo Stevic

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.