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

S. V. Astashkin

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arXiv · 2208.07215

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

S. V. Astashkin

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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 $L_M$.

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S. V. Astashkin. 2022-08-15. The structure of subspaces in Orlicz spaces between $L^1$ and $L^2$. https://arxiv.org/abs/2208.07215

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