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

TL;DR
This paper introduces a new class of function spaces called mixed-norm Herz-type Besov-Triebel-Lizorkin spaces, providing their characterization and embedding properties, which extend existing results in the field.
Contribution
It defines and characterizes mixed-norm Herz-type Besov-Triebel-Lizorkin spaces and establishes improved embedding theorems compared to prior mixed-norm spaces.
Findings
Established $ ext{φ}$-transform characterization of the new spaces.
Proved Sobolev, Franke, and Jawerth embeddings for these spaces.
Extended and improved classical embeddings for mixed-norm Besov and 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 -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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Mathematical Physics Problems · Mathematical Approximation and Integration
