Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (3): 567-577.

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Berezin Transform and Commutativity of Toeplitz Operators on the Hardy Space over the Polydisk

Yu Tao1, Zhuang Chunming2   

  1. 1. School of Mathematics Siences, Dalian University of Technology, Liaoning Dalian 116024;
    2. Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004
  • Received:2013-12-30 Revised:2014-07-04 Online:2015-06-25 Published:2015-06-25

Abstract:

In this paper we discuss the commutativity of Toeplitz operators on the Hardy space over the polydisk. Using the Berezin transform and the harmonic extension, we obtain a necessary and sufficient condition for two Toeplitz operators to commute with each other.

Key words: Berezin transform, Toeplitz operator, Hardy space, Polydisk

CLC Number: 

  • O177.1
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