Variable Besov-type spaces

Abstract

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

Some mistakes are corrected. arXiv admin note: substantial text overlap with arXiv:1508.05980, arXiv:1503.04011, arXiv:1601.00309