Abstract
In this article we introduce Besov-type spaces with variable smoothness and integrability, which unify and generalize the Besov-type spaces with fixed exponents. Under natural regularity assumptions on the exponent functions, we show that our spaces are well-defined, i.e., independent of the choice of basis functions and we establish some properties of these function spaces. Moreover the Sobolev embeddings for these function spaces are obtained.
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