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 $h_{\omega} ^p(R^n)$ with $0<p\leq 1$ and weight $\omega\in A_1(R^n)$. As an application, we prove the boundedness of inhomogeneous Calder\'on-Zygmund operators on $h_{\omega}^p(R^n)$ via weighted local approximate atoms and molecules.