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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
 MSC Classifications: 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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