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

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