Abstract and Applied Analysis
Volume 2008 (2008), Article ID 605807, 8 pages
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

Academic Editor: Stevo Stevic

Copyright © 2008 Xiaohong Fu and Xiangling Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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