Variable Triebel-Lizorkin-type spaces

TL;DR

This paper introduces variable Triebel-Lizorkin-type spaces, establishing their well-defined nature, atomic characterization, and Sobolev embedding properties, advancing the understanding of function spaces with variable smoothness.

Contribution

The paper defines and analyzes Triebel-Lizorkin-type spaces with variable smoothness, providing basis independence, atomic characterization, and Sobolev embedding results.

Findings

Spaces are well-defined and basis-independent.

Atomic characterization of the variable Triebel-Lizorkin spaces.

Sobolev embeddings for these spaces are established.

Abstract

In this paper we study Triebel-Lizorkin-type spaces with variable smoothness and integrability. We show that our space is well-defined, i.e., independent of the choice of basis functions and we obtain their atomic characterization. Moreover the Sobolev embeddings for these function spaces are obtained.