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COMPACT WEIGHTED COMPOSITION OPERATORS BETWEEN $L^{p}$-SPACES

Published online by Cambridge University Press:  16 January 2020

CHING-ON LO*
Affiliation:
Division of Science, Engineering and Health Studies, College of Professional and Continuing Education, The Hong Kong Polytechnic University, Hong Kong email [email protected]
ANTHONY WAI-KEUNG LOH
Affiliation:
Division of Science, Engineering and Health Studies, College of Professional and Continuing Education, The Hong Kong Polytechnic University, Hong Kong email [email protected]

Abstract

We provide complete characterisations for the compactness of weighted composition operators between two distinct $L^{p}$-spaces, where $1\leq p\leq \infty$. As a corollary, when the underlying measure space is nonatomic, the only compact weighted composition map between $L^{p}$-spaces is the zero operator.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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