Besov-type spaces with variable smoothness and integrability II

Abstract

The aim of this paper is to study properties of Besov-type spaces with variable smoothness. We show that these spaces are characterized by the phi-transforms in appropriate sequence spaces and we obtain atomic decompositions for these spaces.

We add the proof of Lemma 2 and we reformulate Lemma 4. Accepted in Annals of Functional Analysis under the title "Some characterizations of variable Besov-type spaces"