Martingale transforms on Banach function spaces

Kwok-Pun Ho; Kwok-Pun Ho

doi:10.3934/era.2022114

Electronic Research Archive

2022, Volume 30, Issue 6: 2247-2262. doi: 10.3934/era.2022114

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Research article

Martingale transforms on Banach function spaces

Kwok-Pun Ho ^,

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

Received: 15 August 2021 Revised: 06 December 2021 Accepted: 20 December 2021 Published: 21 April 2022

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.
- martingale transform,
- Banach function spaces,
- Orlicz spaces,
- Lorentz-Karamata spaces,
- variable Lebesgue spaces,
- Morrey spaces
Citation: Kwok-Pun Ho. Martingale transforms on Banach function spaces[J]. Electronic Research Archive, 2022, 30(6): 2247-2262. doi: 10.3934/era.2022114

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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.

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