
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.
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