Characterization of a class of embeddings for function spaces with Muckenhoupt weights

TL;DR

This paper characterizes when continuous Sobolev embeddings hold for function spaces with Muckenhoupt weights, extending to Jawerth-Franke embeddings and vector-valued spaces, with practical examples.

Contribution

It provides a comprehensive characterization of Sobolev embeddings for weighted function spaces with Muckenhoupt weights, including extensions to other embedding types and examples.

Findings

Characterization of Sobolev embeddings with Muckenhoupt weights

Extensions to Jawerth-Franke embeddings and vector-valued spaces

Examples involving prominent weights

Abstract

For function spaces equipped with Muckenhoupt weights, the validity of continuous Sobolev embeddings in case $p_0\leq p_1$ is characterized. Extensions to Jawerth-Franke embeddings, vector-valued spaces and examples involving some prominent weights are also provided.