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Research Article | Open Access

Martingale transforms on Banach function spaces

Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, Hong Kong, China
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Abstract

We establish the boundedness of martingale transforms on Banach function spaces by using the Rubio de Francia extrapolation theory and the interpolation theorem by Zygmund. The main result also yields the boundedness of the martingale transforms on rearrangement-invariant Banach function spaces, Orlicz spaces, Lorentz-Karamata spaces, Zygmund spaces, Lebesgue spaces with variable exponents, Morrey spaces with variable exponents and Lorentz-Karamata Morrey spaces.

Keywords

martingale transformBanach function spacesOrlicz spacesLorentz-Karamata spacesvariable Lebesgue spacesMorrey spaces

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Electronic Research Archive
Volume 30 Issue 6,
June 2022
Pages 2247-2262
DOI: 10.3934/era.2022114

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Ho K-P. Martingale transforms on Banach function spaces. Electronic Research Archive, 2022, 30(6): 2247-2262. https://doi.org/10.3934/era.2022114

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Received: 15 August 2021
Revised: 06 December 2021
Accepted: 20 December 2021
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)