Generalized Campanato Space Over Non-homogeneous Space and Its Applications

TL;DR

This paper introduces a generalized Campanato space over non-homogeneous spaces, explores its properties, and applies it to establish boundedness results for fractional integral operators and their commutators.

Contribution

It defines a new generalized Campanato space over non-homogeneous spaces and studies its fundamental properties and applications in operator boundedness.

Findings

Established John-Nirenberg inequality for the space

Provided characterizations of the space

Proved boundedness of fractional Marcinkiewicz operators

Abstract

The authors introduce generalized Campanato space with regularized condition over non-homogeneous space, and study its basic properties including the John-Nirenberg inequality and equivalent characterizations. As applications, the boundedness of fractional type Marcinkiewicz integral operator and its commutator on generalized Morrey space over non-homogeneous space is obtained.