Cancellation conditions and boundedness of Inhomogeneous Calder\'on-Zygmund operators on local Hardy spaces associate with spaces of homogeneous type

TL;DR

This paper establishes sufficient cancellation conditions for the boundedness of inhomogeneous Calderón-Zygmund operators on local Hardy spaces over spaces of homogeneous type, introducing new atom and molecule characterizations with moment conditions.

Contribution

It provides novel cancellation criteria and a new approach to atoms and molecules for local Hardy spaces on spaces of homogeneous type.

Findings

Sufficient cancellation conditions for boundedness are identified.

New atom and molecule characterizations with moment conditions are introduced.

The results extend the theory of Calderón-Zygmund operators to more general spaces.

Abstract

In this work, we present sufficient cancellation conditions for the boundedness of inhomogeneous Calder\'on-Zygmund type operators on local Hardy spaces defined over spaces of homogeneous type in the sense of Coifman & Weiss for $ 0<p\leq 1 $. A new approach to atoms and molecules for local Hardy spaces in this setting are introduced with special moment conditions.