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COMPACT WEIGHTED COMPOSITION OPERATORS ON $H^{p}$-SPACES

Part of: Special classes of linear operators Spaces and algebras of analytic functions

Published online by Cambridge University Press:  26 February 2019

CHING-ON LO Open the ORCID record for CHING-ON LO [Opens in a new window]  and
ANTHONY WAI-KEUNG LOH Open the ORCID record for ANTHONY WAI-KEUNG LOH [Opens in a new window]
CHING-ON LO*
Affiliation:
Division of Science and Technology, Hong Kong Community College, The Hong Kong Polytechnic University, Hong Kong email cccolo@hkcc-polyu.edu.hk
ANTHONY WAI-KEUNG LOH
Affiliation:
Division of Science and Technology, Hong Kong Community College, The Hong Kong Polytechnic University, Hong Kong email ccccaloh@hkcc-polyu.edu.hk
*
✉cccolo@hkcc-polyu.edu.hk
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Abstract

Let $u$ and $\unicode[STIX]{x1D711}$ be two analytic functions on the unit disc $D$ such that $\unicode[STIX]{x1D711}(D)\subset D$. A weighted composition operator $uC_{\unicode[STIX]{x1D711}}$ induced by $u$ and $\unicode[STIX]{x1D711}$ is defined by $uC_{\unicode[STIX]{x1D711}}f:=u\cdot f\circ \unicode[STIX]{x1D711}$ for every $f$ in $H^{p}$, the Hardy space of $D$. We investigate compactness of $uC_{\unicode[STIX]{x1D711}}$ on $H^{p}$ in terms of function-theoretic properties of $u$ and $\unicode[STIX]{x1D711}$.

Keywords

weighted composition operatorsHardy spacescompact operators

MSC classification

Primary: 47B33: Composition operators
Secondary: 30H10: Hardy spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 3 , June 2019 , pp. 473 - 484
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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References

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