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

DOI10.1007/S00209-023-03255-0arXiv2208.07215MaRDI QIDQ6407893

Sergey V. Astashkin

Publication date: 15 August 2022

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 $L_M$.

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sequence spaces (including Köthe sequence spaces) (46A45) Isomorphic theory (including renorming) of Banach spaces (46B03) Probabilistic methods in Banach space theory (46B09)

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