The local Morrey-type space Associated with Ball Quasi-Banach Function Spaces and Application

TL;DR

This paper introduces a new class of local Morrey-type spaces linked with ball quasi-Banach function spaces, exploring their properties and boundedness of key operators like Hardy-Littlewood maximal and Hardy operators.

Contribution

It is the first to define and analyze local Morrey-type spaces associated with ball quasi-Banach function spaces, including operator boundedness and decomposition properties.

Findings

Hardy-Littlewood maximal operator is bounded on these spaces.

Nonsmooth decomposition of the spaces is established.

Boundedness of Hardy operator is proved.

Abstract

In this paper, we define for the first time the local Morrey-type space associated with ball quasi-Banach function spaces and show the related series of properties. In addition, Hardy-Littlewood maximal operator's boundedness is proved. We investigate nonsmooth decomposition of the local Morrey-type space associated with ball quasi-Banach function spaces via the Hardy local Morrey-type spaces associated with ball quasi-Banach function spaces. And we consider Hardy operator's boundedness.