VARIABLE BESOV-TYPE SPACES
1 : M'sila University. Department of Mathematics. Laboratory of Functional Analysis and Geometry of Spaces.
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In 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 obtained.