On relatively compact sets in quasi-Banach function spaces

TL;DR

This paper investigates the properties of relatively compact sets in Quasi-Banach function spaces, improving existing results and establishing comprehensive criteria for relative compactness in weighted function spaces.

Contribution

It provides new, more general criteria for relative compactness in Quasi-Banach function spaces without additional assumptions.

Findings

Improved criteria for relative compactness in Quasi-Banach spaces

Extended results to weighted function spaces without extra conditions

Enhanced understanding of compactness properties in quasi-normed function spaces

Abstract

This paper is devoted to the study of the relatively compact sets in Quasi-Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness criteria for function spaces with any weight without any assumption.