Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (2): 304-314.

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Products and Commuting of Toeplitz Operators on the Bergman Space of the Polydisk

Zhiling Sun()   

  1. College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia Tongliao 028000
  • Received:2018-05-21 Online:2020-04-26 Published:2020-05-21
  • Supported by:
    the NSF of Inner Mongolia(2014BS0106);the NSF of Inner Mongolia(2016MS0118);the Foundation of Inner Mongolia University for Nationalities(NMDYB19058)

Abstract:

In this paper, we give some necessary and sufficient conditions for the product of two Toeplitz operators with certain symbols to be a Toeplitz operator and give a formula for the symbol of the product on the Bergman space of polydisk. Next, the corresponding commuting problem of Toeplitz operator is studied. All the results are stated in terms of the Mellin transform of the symbol.

Key words: Toeplitz operators, Bergman space of polydisk, Mellin transform

CLC Number: 

  • O177.1
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