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Embeddings of Besov spaces of logarithmic smoothness. (English) Zbl 1325.46039
Summary: This paper deals with Besov spaces of logarithmic smoothness \(B_{p,r}^{0,b}\) formed by periodic functions. We study embeddings of \(B_{p,r}^{0,b}\) into Lorentz-Zygmund spaces \(L_{p,q}(\log L)_{\beta }\). Our techniques rely on the approximation structure of \(B_{p,r}^{0,b}\), Nikol’skiĭ type inequalities, extrapolation properties of \(L_{p,q}(\log L)_{\beta }\) and interpolation.

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
46B70 Interpolation between normed linear spaces
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