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New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk

  Published:2013-11-26
 Printed: Dec 2014
  • Zhong-Shan Fang,
    Department of Mathematics, Tianjin Polytechnic University, Tianjin Tianjin 300387, P.R. China.
  • Ze-Hua Zhou,
    Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China.
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Abstract

We give some new characterizations for compactness of weighted composition operators $uC_\varphi$ acting on Bloch-type spaces in terms of the power of the components of $\varphi,$ where $\varphi$ is a holomorphic self-map of the polydisk $\mathbb{D}^n,$ thus generalizing the results obtained by Hyvärinen and Lindström in 2012.
Keywords: weighted composition operator, compactness, Bloch type spaces, polydisk, several complex variables weighted composition operator, compactness, Bloch type spaces, polydisk, several complex variables
MSC Classifications: 47B38, 47B33, 32A37, 45P05, 47G10 show english descriptions Operators on function spaces (general)
Composition operators
Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]
Integral operators [See also 47B38, 47G10]
Integral operators [See also 45P05]
47B38 - Operators on function spaces (general)
47B33 - Composition operators
32A37 - Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]
45P05 - Integral operators [See also 47B38, 47G10]
47G10 - Integral operators [See also 45P05]
 

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