Compactness criteria for Stieltjes function spaces and applications

TL;DR

This paper investigates topological properties of Stieltjes function spaces, focusing on compactness criteria and their implications for Stieltjes-Sobolev spaces and decomposable functions, advancing the understanding of these specialized function spaces.

Contribution

It introduces new compactness criteria for Stieltjes function spaces and explores their applications in Stieltjes-Sobolev spaces and decomposable functions.

Findings

Established compactness results analogous to Ascoli-Arzelà and Kolmogorov-Riesz theorems.

Applied these results to Stieltjes-Sobolev spaces.

Analyzed properties of decomposable functions within this framework.

Abstract

In this work we study some topological aspects of function spaces arising in Stieltjes differential calculus. Chief among them are compactness results related to the Ascoli-Arzel\`a and Kolmogorov-Riesz theorems, as well as their applications to Stieltjes-Sobolev spaces and decomposable functions.