Absolutely continuous embeddings between spaces of functions

Abstract

Absolute continuity of an embedding between Banach function spaces is an interesting property which is closely related to compactness. In this paper we study absolutely continuous embeddings between arbitrary Banach spaces intermediate with respect to the couple $(L_{1}(\Omega), L_{\infty}(\Omega))$. Our results allow to check if an embedding of such spaces is absolutely continuous. Applications related with the degree of proximity between two function spaces are established for the case $\Omega=[0,1]$ and $\Omega=[0,\infty)$.