On the Interplay of Regularity and Decay in Case of Radial Functions I. Inhomogeneous spaces

TL;DR

This paper investigates how regularity and decay properties of radial functions in Besov and Lizorkin-Triebel spaces interact, using atomic decompositions and trace theorems to analyze their boundedness and decay behaviors.

Contribution

It provides new insights into the relationship between regularity and decay for radial functions in these function spaces, employing novel analytical tools.

Findings

Decay and regularity are intricately linked in radial functions.

Atomic decompositions effectively analyze decay properties.

Trace theorems reveal the interplay between regularity and decay.

Abstract

We deal with decay and boundedness properties of radial functions belonging to Besov and Lizorkin-Triebel spaces. In detail we investigate the surprising interplay of regularity and decay. Our tools are atomic decompositions in combination with trace theorems.