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Extrapolation to weighted Morrey spaces with variable exponents and applications

Part of: Harmonic analysis in several variables Miscellaneous topics - Partial differential equations Integral, integro-differential, and pseudodifferential operators Nontrigonometric harmonic analysis Linear function spaces and their duals

Published online by Cambridge University Press:  09 November 2021

Kwok-Pun Ho Open the ORCID record for Kwok-Pun Ho [Opens in a new window]
Kwok-Pun Ho*
Affiliation:
Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, Hong Kong, China([email protected])
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Abstract

This paper establishes the mapping properties of pseudo-differential operators and the Fourier integral operators on the weighted Morrey spaces with variable exponents and the weighted Triebel–Lizorkin–Morrey spaces with variable exponents. We obtain these results by extending the extrapolation theory to the weighted Morrey spaces with variable exponents. This extension also gives the mapping properties of Calderón–Zygmund operators on the weighted Hardy–Morrey spaces with variable exponents and the wavelet characterizations of the weighted Hardy–Morrey spaces with variable exponents.

Keywords

Morrey spacesTriebel–Lizorkin spacesHardy–Morrey spacesextrapolationpseudo-differential operatorsFourier integral operatorsCalderón–Zygmund operatorswavelets

MSC classification

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B35: Function spaces arising in harmonic analysis 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47G30: Pseudodifferential operators 35S30: Fourier integral operators
Secondary: 42B30: $H^p$-spaces 42C40: Wavelets and other special systems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 4 , November 2021 , pp. 1002 - 1027
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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