Composition Operator from Weighted Bergman Space to Logarithmic Bloch Space on the Unit Polydisc

Composition Operator from Weighted Bergman Space to Logarithmic Bloch Space on the Unit Polydisc

Qiuhe Huang 

Department of Mathematics, Lushan Collge of Guangxi University of Science and Technology, Liuzhou, Guangxi 545616, China

Corresponding Author Email: 
huanghe725@163.com
Page: 
310-321
|
DOI: 
https://doi.org/10.18280/ama_a.540213
Received: 
7 June 2017
| |
Accepted: 
20 June 2017
| | Citation

OPEN ACCESS

Abstract: 

This paper introduces the logarithmic Bloch space $B_{\log }^{q}\left(D^{n}\right)$, a new space of analytic functions on the unit polydisc, investigates the composition operator $C_{\varphi}$ from weighted Bergman space to logarithmic Bloch space on the unit polydisc, and provides the sufficient and necessary conditions to ensure the boundedness and compactness of the composition operator $C_{\varphi}$ from weighted Bergman space to logarithmic Bloch space.

Keywords: 

Composition operator, Weighted Bergman space, Logarithmic Bloch space, Boundedness, Compactness.

1. Introduction
2. Auxiliary Results
3. Main Results and Proofs
Acknowledgments

The author wishes to thank the science project of Higher Education of GuangXi in China for contract KY2015LX778, under which the present work was possible.

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