Homogeneity property of Besov and Triebel-Lizorkin spaces

TL;DR

This paper investigates the homogeneity property of Besov and Triebel-Lizorkin spaces with bounded support, providing new insights into their structure, embeddings, and applications in pointwise multipliers.

Contribution

It establishes a homogeneity property for these function spaces and explores related compact embeddings and entropy numbers, with applications to pointwise multipliers.

Findings

Proved homogeneity property for functions with bounded support in Besov and Triebel-Lizorkin spaces.

Analyzed entropy numbers of embeddings between these spaces.

Applied results to pointwise multiplier problems.

Abstract

We consider the classical Besov and Triebel-Lizorkin spaces defined via differences and prove a homogeneity property for functions with bounded support in the frame of these spaces. As the proof is based on compact embeddings between the studied function spaces we present also some results on the entropy numbers of these embeddings. Moreover, we derive some applications in terms of pointwise multipliers.