ON SUBSPACES OF AN ORLICZ SPACE SPANNED BY INDEPENDENT IDENTICALLY DISTRIBUTED FUNCTIONS

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Abstract

Subspaces of an Orlicz space LM generated by probabilistically independent copies of a function \(f \in {{L}_{M}}\), \(\int_0^1 {f(t){\kern 1pt} dt} = 0\), are studied. In terms of dilations of f, we get a characterization of strongly embedded subspaces of this type and obtain conditions that guarantee that the unit ball of such a subspace has equi-absolutely continuous norms in LM. A class of Orlicz spaces such that for all subspaces generated by independent identically distributed functions these properties are equivalent and can be characterized by Matuszewska–Orlicz indices is determined.

About the authors

S. V. Astashkin

Samara National Research University; Lomonosov Moscow State University; Moscow Сenter of Fundamental and Applied Mathematics; Bahcesehir University

Author for correspondence.
Email: astash@ssau.ru
Russian Federation, Samara; Russian Federation, Moscow; Russian Federation, Moscow; Turkey, Istanbul

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