Mixed-norm Herz-type Besov spaces

Abstract

In this paper, we introduce mixed-norm Herz-type Besov spaces and establish their $\phi$-transform characterization in the sense of Frazier and Jawerth. We also prove Sobolev embedding theorems for these spaces. The resulting embeddings extend and improve several known embedding results for mixed-norm Besov spaces.

arXiv commentDue to the technical nature of the subject, we have divided the work into three parts: "Mixed-Norm Herz-Type Besov Spaces", "Mixed-Norm Herz-Type Triebel-Lizorkin Spaces", and "Jawerth-Franke Embeddings for Mixed-Norm Herz-Type Besov and Triebel-Lizorkin Spaces". This division allows for a clearer and more systematic presentation of the results and proofs