Variable Besov-type spaces

TL;DR

This paper introduces variable Besov-type spaces, characterizes them via $\, ext{ extphi}$-transforms, provides atomic decompositions, and explores Sobolev embeddings, expanding the understanding of function spaces with variable smoothness.

Contribution

The paper develops a new class of Besov-type spaces with variable parameters, offering novel characterizations and embedding results.

Findings

Spaces characterized by $\, extphi$-transforms

Atomic decompositions established

Sobolev embeddings derived

Abstract

In this paper we introduce Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the $\varphi $-transforms in appropriate sequence spaces and we obtain atomic decompositions for these spaces. Moreover the Sobolev embeddings for these function spaces are obtained.