Tokyo Journal of Mathematics

$B_w^u$-function Spaces and Their Interpolation

Eiichi NAKAI and Takuya SOBUKAWA

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We introduce $B_w^u$-function spaces which unify Lebesgue, Morrey-Campanato, Lipschitz, $B^p$, $\mathrm{CMO}$, local Morrey-type spaces, etc., and investigate the interpolation property of $B_w^u$-function spaces. We also apply it to the boundedness of linear and sublinear operators, for example, the Hardy-Littlewood maximal and fractional maximal operators, singular and fractional integral operators with rough kernel, the Littlewood-Paley operator, Marcinkiewicz operator, and so on.

Article information

Tokyo J. Math., Volume 39, Number 2 (2016), 483-516.

First available in Project Euclid: 30 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B35: Function spaces arising in harmonic analysis 46B70: Interpolation between normed linear spaces [See also 46M35]
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory


NAKAI, Eiichi; SOBUKAWA, Takuya. $B_w^u$-function Spaces and Their Interpolation. Tokyo J. Math. 39 (2016), no. 2, 483--516. doi:10.3836/tjm/1459367270.

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