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

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 φ-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev embeddings. Our embeddings extend and improve Sobolev embeddings of mixed-norm Besov and Triebel-Lizorkin spaces.