Jawerth-Franke embeddings of Herz-type Besov and Triebel-Lizorkin 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, and we prove the necessity of some assumptions on the parameters. As an application we present new embeddings between Besov and Herz spaces.