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Besov-Köthe spaces and application. (English) Zbl 1273.46018

Summary: We introduce and study the family of Besov-Köthe spaces which is a generalization of the Besov spaces, the Besov-Morrey spaces and the variable Besov spaces. As an application of the general results for the Besov-Köthe spaces, we identify a pre-dual of the Besov-Morrey space.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
42B25 Maximal functions, Littlewood-Paley theory
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42B35 Function spaces arising in harmonic analysis