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Atomic decompositions of martingale Hardy Lorentz amalgam spaces and applications

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Abstract

We develop the martingale theory in the framework of Lorentz amalgam spaces. Atomic decompositions for the martingale Hardy Lorentz amalgam spaces are established. As applications of atomic decompositions, the dual spaces of the martingale Hardy Lorentz amalgam spaces are characterized. Furthermore, when the stochastic basis is regular, the boundedness of the fractional integrals on martingale Hardy Lorentz amalgam spaces is proved. The results obtained here generalized the corresponding known results in martingale Hardy amalgam spaces and various classical martingale Hardy spaces.

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Authors and Affiliations

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

    L. Li & Y. Wang

  2. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, People’s Republic of China

    A. Yang

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  1. L. Li
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  2. Y. Wang
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  3. A. Yang
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Correspondence to A. Yang.

Additional information

Anming Yang is supported by the NSFC (No. 11801157) and Hunan Provincial Natural Science Foundation (No. 2020JJ5030).

Libo Li is supported by the NSFC (No. 12101223) and Hunan Provincial Natural Science Foundation (No. 2022JJ40146).

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Li, L., Wang, Y. & Yang, A. Atomic decompositions of martingale Hardy Lorentz amalgam spaces and applications. Acta Math. Hungar. (2024). https://doi.org/10.1007/s10474-024-01422-1

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  • DOI: https://doi.org/10.1007/s10474-024-01422-1

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