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

Autor:	Astashkin, S. V.
Rok vydání:	2022
Předmět:	Mathematics - Functional Analysis 46E30 46B03 46B09 46A45
Druh dokumentu:	Working Paper
Popis:	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 $L_M$. Comment: 24 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.07215 Zobrazit plný text záznamu View this record from Arxiv