# The Kolmogorov-Riesz Theorem and Some Compactness Criterions of Bounded Subsets in Weighted Variable Exponent Amalgam and Sobolev Spaces

## TL;DR

This paper investigates the properties of totally bounded sets in weighted variable exponent amalgam and Sobolev spaces, providing generalized compactness criteria to enhance understanding of their structure.

## Contribution

It introduces new generalized compactness criteria for totally bounded subsets in weighted variable exponent amalgam and Sobolev spaces.

## Key findings

- Characterization of totally bounded sets in these spaces
- Generalized compactness criteria established
- Enhanced understanding of space structure

## Abstract

We study totally bounded subsets in weighted variable exponent amalgam and Sobolev spaces. Moreover, this paper includes several detailed generalized results of some compactness criterions in these spaces.