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We introduce a new class of weighted local approximate atoms includingclassical weighted local atoms. Then we further obtain the weighted localapproximate 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.

New Atomic Decompositions of Weighted Local Hardy Spaces