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.