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ON PROPERTIES OF SPACES WITH MARTINGALE MIXED NORM WITH SUMMABILITY EXPONENTS CLOSE TO ONE

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Abstract

For spaces of random variables with martingale mixed norm the theorem of A. Pelczynski on the absence of an unconditional basis in the space \(L_1(0,1)\) is generalized and (in terms of summability exponents) the cases are studied when these spaces coincide with the space \(L_1\). 2020 Mathematics subject classification: Primary 60G46; Secondary 60G42, 46E30.

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References

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Funding

This research was supported by the Ministry of Science and Education of Russian Federation, grant N 075-02-2022-893.

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Authors and Affiliations

  1. Regional Mathematical Center of Southern Federal University, 105/42, Bolshaya Sadovaya Str., Rostov-on-Don, Russia

    Igor V. Pavlov

  2. Don State Technical University, 1, Gagarina Squ., Rostov-on-Don, Russia

    Igor V. Pavlov

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  1. Igor V. Pavlov
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Correspondence to Igor V. Pavlov.

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Pavlov, I.V. ON PROPERTIES OF SPACES WITH MARTINGALE MIXED NORM WITH SUMMABILITY EXPONENTS CLOSE TO ONE. J Math Sci 271, 126–135 (2023). https://doi.org/10.1007/s10958-023-06327-y

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  • DOI: https://doi.org/10.1007/s10958-023-06327-y

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