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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 506, Pages 16–19
DOI: https://doi.org/10.31857/S2686954322050034 (Mi danma290) 		 
MATHEMATICS

Binary Orlicz spaces

S. V. Astashkin

Samara National Research University, Samara, Russia
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DOI: https://doi.org/10.31857/S2686954322050034
Abstract: A subspace $H$ of a rearrangement invariant space $X$ is strongly embedded in $X$ if, on $H$, convergence in the $X$-norm is equivalent to convergence in measure. Necessary and sufficient conditions on an Orlicz function $M$ are obtained under which the unit ball of any subspace strongly embedded in the Orlicz space $L_M$ has equi-absolutely continuous norms in $L_M$.
Keywords: rearrangement invariant space, strongly embedded subspace, Orlicz function, Orlicz space, Matuszewska–Orlicz indices.
Funding agency Grant number
Program of developing the Scientific and Educational Mathematical Center of the Volga Federal District 075-02-2022-878
This work was performed within the program of developing the Scientific and Educational Mathematical Center of the Volga Federal District, agreement no. 075-02-2022-878.
Presented: B. S. Kashin
Received: 13.05.2022
Revised: 02.08.2022
Accepted: 10.08.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 2, Pages 315–317
DOI: https://doi.org/10.1134/S1064562422050052
Bibliographic databases:
Document Type: Article
UDC: 517.982.27
Language: Russian
Citation: S. V. Astashkin, “Binary Orlicz spaces”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 16–19; Dokl. Math., 106:2 (2022), 315–317
Citation in format AMSBIB
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\jour Dokl. Math.
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