Variable Besov-type spaces

Published 17 Jan 2021 in math.FA | (2101.06670v2)

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.

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