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\(B_w^u\)-function spaces and their interpolation. (English) Zbl 1365.42016

In this paper the authors define some function space \(B^u_w\) which is a generalization of the 2-microlocal type Morrey space given in [Y. Komori-Furuya et al., J. Funct. Spaces Appl. 2013, Article ID 859402, 21 p. (2013; Zbl 1275.42036)]. They investigate the interpolation property of the \(B^u_w\) function space. As an application, the authors also consider the boundedness of linear and sublinear operators on these function spaces.

MSC:

42B35 Function spaces arising in harmonic analysis
46B70 Interpolation between normed linear spaces
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B25 Classical Banach spaces in the general theory

Citations:

Zbl 1275.42036
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