$B_w^u$-function spaces and their interpolation

TL;DR

This paper introduces a new class of function spaces called $B_w^u$, unifying many classical spaces, and studies their interpolation properties and applications to the boundedness of various integral operators.

Contribution

The paper defines $B_w^u$-function spaces that unify multiple classical function spaces and explores their interpolation properties and operator boundedness applications.

Findings

$B_w^u$-spaces unify Lebesgue, Morrey, Lipschitz, and other classical spaces.

Interpolation properties of $B_w^u$-spaces are established.

Boundedness of key operators like Hardy-Littlewood maximal and fractional integral operators is proved.

Abstract

We introduce $B_w^u$-function spaces which unify Lebesgue, Morrey-Campanato, Lipschitz, $B^p$, 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.