Table of Contents
Journal of Operators
Volume 2013 (2013), Article ID 154029, 9 pages
http://dx.doi.org/10.1155/2013/154029
Research Article

Weighted Composition Operators from the Bloch Space and the Analytic Besov Spaces into the Zygmund Space

1Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
2Department of Mathematics, Jiaying University, Meizhou, Guangdong 514015, China

Received 25 February 2013; Accepted 19 April 2013

Academic Editor: Zeljko Cuckovic

Copyright © 2013 Flavia Colonna and Songxiao Li. 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.

Abstract

We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space and the analytic Besov spaces (with ) into the Zygmund space . As a special case, we show that the bounded (resp., compact) composition operators from , , and to coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.