Abstract and Applied Analysis
Volume 2007 (2007), Article ID 48478, 13 pages
Weighted Composition Operators from to the Bloch Space on the Polydisc
1Department of Mathematics, Shantou University, Shantou 515063, GuangDong, China
2Department of Mathematics, JiaYing University, Meizhou 514015, GuangDong, China
3Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000, Serbia
Received 9 February 2007; Revised 16 April 2007; Accepted 3 May 2007
Academic Editor: Ferhan Merdivenci Atici
Copyright © 2007 Songxiao Li and Stevo Stević. 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 be the unit polydisc of , be a holomorphic self-map of , and a holomorphic function on . Let denote the space of all holomorphic functions with domain , the space of all bounded holomorphic functions on , and the Bloch space, that is, . We give necessary and sufficient conditions for the weighted
composition operator induced by and to be bounded and compact from to the Bloch space .