## Tokyo Journal of Mathematics

### $B_w^u$-function Spaces and Their Interpolation

#### Abstract

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

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

Dates
First available in Project Euclid: 30 March 2016

https://projecteuclid.org/euclid.tjm/1459367270

Digital Object Identifier
doi:10.3836/tjm/1459367270

Mathematical Reviews number (MathSciNet)
MR3599505

Zentralblatt MATH identifier
1365.42016

#### Citation

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