The structure of subspaces in Orlicz spaces between $L^1$ and $L^2$

S. V. Astashkin

The structure of subspaces in Orlicz spaces between $L^1$ and $L^2$

Functional Analysis 2022-08-16 v1

Authors: S. V. Astashkin

Abstract

A subspace $H$ of a rearrangement invariant space $X$ on $[0,1]$ is strongly embedded in $X$ if, in $H$ , convergence in $X$ -norm is equivalent to convergence in measure. We obtain necessary and sufficient conditions on an Orlicz function $M$ , under which the unit ball of an arbitrary strongly embedded subspace in the Orlicz space $L_M$ has equi-absolutely continuous norms in $L_M$ .

Keywords

orlicz space rearrangement invariant space strongly embedded subspace equi-absolutely continuous norm convergence in measure

Cite

@article{arxiv.2208.07215,
  title  = {The structure of subspaces in Orlicz spaces between $L^1$ and $L^2$},
  author = {S. V. Astashkin},
  journal= {arXiv preprint arXiv:2208.07215},
  year   = {2022}
}

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24 pages

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