Invertible Toeplitz Operators Products on the Bergman Space of the Polydisk
Received:May 04, 2011  Revised:August 31, 2011
Key Words: Toeplitz operators   Bergman space   polydisk   reverse H\"{o}lder inequality.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10971020).
Author NameAffiliation
Zhingling SUN School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia 028000, P. R. China 
Yufeng LU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
 
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Abstract:
      We prove a reverse H\"{o}lder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk. Next, we further describe when for which square integrable analytic functions $f$ and $g$ on the polydisk the densely defined products $T_{f}T_{\bar{g}}$ are bounded invertible Toeplitz operators.
Citation:
DOI:10.3770/j.issn:2095-2651.2012.05.003
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