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

TL;DR

This paper characterizes when subspaces of Orlicz spaces between L^1 and L^2 are strongly embedded, focusing on conditions for the unit ball to have equi-absolutely continuous norms.

Contribution

It provides necessary and sufficient conditions on Orlicz functions for subspaces to be strongly embedded with equi-absolutely continuous norms.

Findings

Characterization of strong embedding in Orlicz spaces

Conditions on Orlicz functions for equi-absolutely continuous norms

Analysis of subspace structure between L^1 and L^2

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 $L_M$.