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Grand martingale Hardy spaces for \(0<p\le 1\)

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Abstract

In this paper, we develop the martingale theory in the framework of grand Lebesgue spaces for \(0<p\le 1\). Atomic decompositions for the grand martingale Hardy spaces are established. With the help of the atomic decompositions, the dual spaces of the grand martingale Hardy spaces are characterized and some martingale inequalities are deduced. Furthermore, when the stochastic basis is regular, the boundedness of the fractional integrals on grand martingale Hardy spaces is proved. The results obtained here unify and generalize the previous results of grand martingale Hardy spaces.

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Acknowledgements

The authors would like to express their gratitude to the referee for his/her careful reading and useful comments. Zhiwei Hao is supported by the NSFC (No. 11801001). Libo Li is supported by the NSFC (No. 12101223). Anming Yang is supported by the NSFC (No. 11801157) and Hunan Provincial Natural Science Foundation (No. 2020JJ5030).

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, 411201, People’s Republic of China

    Zhiwei Hao & Libo Li

  2. School of Mathematics, Hunan University, Changsha, 410082, People’s Republic of China

    Anming Yang

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  1. Zhiwei Hao
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  2. Libo Li
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  3. Anming Yang
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Correspondence to Anming Yang.

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Communicated by Yong Jiao.

The original online version of this article was revised: The original version of this article, published on 03 September 2022, unfortunately contained a mistake. Due to an error in the typesetting process, the title of the PDF version of this article was incorrectly given as “Grand martingale Hardy spaces for 0 < p ≤ 10 < p ≤ 1” but should have been “Grand martingale Hardy spaces for 0 < p ≤ 1”.

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Hao, Z., Li, L. & Yang, A. Grand martingale Hardy spaces for \(0<p\le 1\). Ann. Funct. Anal. 13, 66 (2022). https://doi.org/10.1007/s43034-022-00213-5

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