Abstract and Applied Analysis
Volume 2008 (2008), Article ID 538573, 7 pages
doi:10.1155/2008/538573
Research Article
A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit
Ball
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
Received 13 June 2008; Revised 12 October 2008; Accepted 20 November 2008
Academic Editor: Stevo Stevic
Copyright © 2008 Yufeng Lu and Jun Yang. 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
This paper shows that if S is a bounded linear operator acting on
the weighted Bergman spaces Aα2 on the unit ball in ℂn such that STzi=Tz¯iS (i=1,…,n), where Tzi=zif and
Tz¯i=P(z¯if); and where P is the weighted Bergman projection, then S must be a Hankel operator.