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THE HILBERT–SCHMIDT NORM OF A COMPOSITION OPERATOR ON THE BERGMAN SPACE

Part of: Special classes of linear operators Holomorphic functions of several complex variables Spaces and algebras of analytic functions

Published online by Cambridge University Press:  02 November 2016

CHENG YUAN  and
ZE-HUA ZHOU
CHENG YUAN
Affiliation:
Institute of Mathematics, School of Science, Tianjin University of Technology and Education, Tianjin 300222, PR China email yuancheng1984@163.com
ZE-HUA ZHOU*
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300354, PR China email zehuazhoumath@aliyun.com, zhzhou@tju.edu.cn
*
✉zehuazhoumath@aliyun.com
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Abstract

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We use a generalised Nevanlinna counting function to compute the Hilbert–Schmidt norm of a composition operator on the Bergman space $L_{a}^{2}(\mathbb{D})$ and weighted Bergman spaces $L_{a}^{1}(\text{d}A_{\unicode[STIX]{x1D6FC}})$ when $\unicode[STIX]{x1D6FC}$ is a nonnegative integer.

Keywords

Bergman spacecomposition operatorscounting functions

MSC classification

Primary: 30H20: Bergman spaces, Fock spaces
Secondary: 32A36: Bergman spaces 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) 47B33: Composition operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 2 , April 2017 , pp. 250 - 259
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

Cheng Yuan is supported by the National Natural Science Foundation of China (Grant No. 11501415); Ze-Hua Zhou is supported by the National Natural Science Foundation of China (Grant No. 11371276).

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