New atomic decompositions of weighted local Hardy spaces

Abstract

We introduce a new class of weighted local approximate atoms including classical weighted local atoms. Then we further obtain the weighted local approximate atomic decompositions of weighted local Hardy spaces $h_{\omega }^p\left(R^n\right)$ with $0<p\le 1$ and weight $\omega \in A_1\left(R^n\right)$. As an application, we prove the boundedness of inhomogeneous Calderón–Zygmund operators on $h_{\omega }^p\left(R^n\right)$ via weighted local approximate atoms and molecules.