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Martingale transforms and fractional integrals on rearrangement-invariant martingale Hardy spaces

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Abstract

We establish an interpolation result for the rearrangement-invariant martingale Hardy spaces. By using this interpolation result, we extend the mapping properties of the martingale transforms and the fractional integrals on martingale function spaces. In particular, we obtain the mapping properties on the martingale Hardy–Orlicz spaces, the grand martingale Hardy spaces and the martingale Hardy–Lorentz–Karamata spaces.

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Acknowledgements

The author would like to thank the reviewers for careful reading of the paper and valuable suggestions.

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

    Kwok-Pun Ho

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Ho, KP. Martingale transforms and fractional integrals on rearrangement-invariant martingale Hardy spaces. Period Math Hung 81, 159–173 (2020). https://doi.org/10.1007/s10998-020-00318-1

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