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ESSENTIAL COMMUTATIVITY OF SOME INTEGRAL AND COMPOSITION OPERATORS

Published online by Cambridge University Press:  20 October 2011

ZE-HUA ZHOU*
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China (email: [email protected])
LIANG ZHANG
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China (email: [email protected])
HONG-GANG ZENG
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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In general, multiplication of operators is not essentially commutative in an algebra generated by integral-type operators and composition operators. In this paper, we characterize the essential commutativity of the integral operators and composition operators from a mixed-norm space to a Bloch-type space, and give a complete description of the universal set of integral operators. Corresponding results for boundedness and compactness are also obtained.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The first author was supported in part by the National Natural Science Foundation of China (Grant Nos. 10971153, 10671141).

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