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Compact embeddings of Besov spaces involving only slowly varying smoothness. (English) Zbl 1249.46026
Summary: We characterize compact embeddings of Besov spaces \(B^{0,b}_{p,r}(\mathbb {R}^n)\) involving the zero classical smoothness and a slowly varying smoothness \(b\) into Lorentz-Karamata spaces \(L_{p,q;\bar {b}}(\Omega )\), where \(\Omega \) is a bounded domain in \(\mathbb {R}^n\) and \(\bar {b}\) is another slowly varying function.

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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