Zouheyr ZEGHAD2022-12-182022-12-182022http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/35233In this paper we introduce Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the ϕ-transforms in appropriate sequence spaces and we obtain atomic decompositions for these spaces. Moreover the Sobolev embeddings for these function spaces are obtainedAtom, embeddings, Besov space, maximal function, variable exponentArticle