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

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

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 sub...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-04, Vol.271 (2), p.126-135
1. Verfasser: Pavlov, Igor V.
Format: Artikel
Sprache:eng
Schlagworte:
Exponents
Martingales
Mathematical analysis
Mathematics
Mathematics and Statistics
Random variables
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Zusammenfassung: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06327-y