The Characterization of Radial Subspaces of Besov- and Lizorkin-Triebel Spaces by Differences

TL;DR

This paper investigates how radial subspaces of Besov and Lizorkin-Triebel spaces on  can be characterized using difference operators, extending previous research in this area.

Contribution

It provides new characterizations of radial subspaces of Besov and Lizorkin-Triebel spaces via differences, advancing the understanding of their structure.

Findings

Radial subspaces characterized by differences

Extension of previous characterizations

Deeper insight into the structure of these function spaces

Abstract

We continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on $\R^d$. This time we study characterizations of these subspaces by differences.