Almost compact embeddings between Orlicz and Lorentz spaces

Abstract

We characterize when an Orlicz space $L^A$ is almost compactly (uniformly absolutely continuously) embedded into a Lorentz space $L^{p,q}$ in terms of a balance condition involving parameters $p,q\in[1,\infty]$, and a Young function $A$. In the course of the proof, we develop a new method based on an inequality of Young type involving the measure of level sets of a given function.