Products of Toeplitz Operator on the Weighted Bergman Space of the Unit Ball
Received:April 15, 2010  Revised:April 18, 2011
Key Words: Toeplitz operator   Bergman space   unit ball   Hankel operator.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10971020) and Doctoral Fund of Ministry of Education of China (RFDP).
Author NameAffiliation
Kan ZHANG School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China
College of Sciences, Shenyang Agricultural University, Liaoning 110866, P. R. China 
Yufeng LU School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China
 
Hits: 3333
Download times: 2530
Abstract:
      We consider the question for what kind of square integrable holomorphic functions $f$, $g$ on the unit ball the densely defined products $T_{f}T_{\bar{g}}$ are invertible and Fredholm on the weighted Bergman space of the unit ball. We furthermore obtain necessary and sufficient conditions for bounded Haplitz products $H_{f}T_{\bar{g}}$, where $f\in L^{2}(B_{n}, \d v_{\alpha})$ and $g$ is a square integrable holomorphic function.
Citation:
DOI:10.3770/j.issn:2095-2651.2012.04.008
View Full Text  View/Add Comment