Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces

TL;DR

This paper investigates the properties of embeddings between weighted radial Besov and Triebel-Lizorkin spaces, focusing on continuity and compactness, using wavelet expansions adapted to radial functions.

Contribution

It introduces a discretization method via wavelet expansions tailored for radial functions to analyze embedding properties in weighted spaces.

Findings

Established conditions for continuity of embeddings.

Characterized when embeddings are compact.

Developed a wavelet-based discretization approach.

Abstract

We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class $A_\infty$. The main tool is a discretization in terms of an almost orthogonal wavelet expansion adapted to the radial situation.