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 hωp(Rn) with 0<p≤1 and weight ω∈A1(Rn). As an application, we prove the boundedness of inhomogeneous Calder\'on-Zygmund operators on hωp(Rn) via weighted local approximate atoms and molecules.
@article{arxiv.2309.00899,
title = {New Atomic Decompositions of Weighted Local Hardy Spaces},
author = {Haijing Zhao and Xuechun Yang and Baode Li},
journal= {arXiv preprint arXiv:2309.00899},
year = {2023}
}