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

Published online by Cambridge University Press:  20 November 2018

Zhong-Shan Fang  and
Ze-Hua Zhou
Zhong-Shan Fang
Affiliation:
Department of Mathematics, Tianjin Polytechnic University, Tianjin Tianjin 300387, P.R. China. e-mail: [email protected]
Ze-Hua Zhou
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China. e-mail: [email protected]@tju.edu.cn
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Abstract

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We give some new characterizations for compactness of weighted composition operators $u{{C}_{\varphi }}$ 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

47B3847B3332A3745P0547G10weighted composition operatorcompactnessBloch type spacespolydiskseveral complex variables
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 4 , 01 December 2014 , pp. 794 - 802
Copyright
Copyright © Canadian Mathematical Society 2014

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