Mixed-norm Herz-type Besov-Triebel-Lizorkin spaces

Abstract: Based on mixed-norm Herz spaces, Besov and Triebel-Lizorkin spaces, we introduce the so called mixed-norm Herz-type Besov-Triebel-Lizorkin spaces. We present the $\varphi $-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev, Franke and Jawerth embeddings. Our embeddings extend and improve Sobolev, Franke and Jawerth embeddings of mixed-norm Besov and Triebel-Lizorkin spaces.