Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (3): 521-529.

• Articles • Previous Articles     Next Articles

Hausdorff-type Operator on Bloch Space in the Unit Polydisk in Cn

 HU Rong1, XIE Li2, HU Peng-Yan3   

  1. 1.Department of Mathematics and Finance-Economics, Sichuan Univerity of Arts and Science, Sichuan |Dazhou 635000|2.College of Mathematics and Information, China West Normal University, Sichuan Nanchong |637000|3.College of Mathematics and Computational Science of Shenzhen University, Guangdong Shenzhen |518060
  • Received:2010-11-02 Revised:2011-08-12 Online:2012-06-25 Published:2012-06-25
  • Supported by:

    国家自然科学基金(10571121)和广东省自然科学基金(5010509)资助

Abstract:

In this paper, we define the Hausdorff-type operator Hαμ and its adjoint operator Aαμ on the polydisk and discuss the sufficient conditions
of the boundedness of them. We also obtain an upper bound for the operator norm on Bloch space.

Key words: Unit polydisk, Bloch space, Hausdorff-type operator, Weighted composition operator

CLC Number: 

  • 47B38
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