Amalgam approach to compactness in (quasi-)Banach function spaces

Abstract

We present amalgam-type characterisations of compactness in quasi-Banach function spaces. We further treat, in the same spirit, several related topics, namely convergence, (uniform) absolute continuity of the norm, and almost-compact embeddings. We also treat the case of rearrangement-invariant spaces and show that most of our conditions can be formulated in terms of the non-increasing rearrangement and the representation space.