Jawerth-Franke embeddings of Herz-type Besov and Triebel-Lizorkin spaces

TL;DR

This paper establishes new embedding theorems for Herz-type Besov and Triebel-Lizorkin spaces, including weighted versions, and explores their implications for embeddings between Besov and Herz spaces.

Contribution

It introduces the Jawerth-Franke embeddings for Herz-type Besov and Triebel-Lizorkin spaces, extending known results to weighted cases and linking different function spaces.

Findings

Proved embeddings for Herz-type Besov and Triebel-Lizorkin spaces.

Extended embeddings to spaces with power weights.

Established new relations between Besov and Herz spaces.

Abstract

In this paper we prove the Jawerth-Franke embeddings of Herz-type Besov and Triebel-Lizorkin spaces. Moreover, we obtain the Jawerth-Franke embeddings of Besov and Triebel-Lizorkin spaces equipped with power weights. An application we present new embeddings between Besov and Herz spaces.