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 LM has equi-absolutely continuous norms in LM.
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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.
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Translated by I. Ruzanova
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Astashkin, S.V. Binary Orlicz Spaces. Dokl. Math. 106, 315–317 (2022). https://doi.org/10.1134/S1064562422050052
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DOI: https://doi.org/10.1134/S1064562422050052