We establish the boundedness of the multilinear Calderón-Zygmund operators from a product of weighted Hardy spaces into a weighted Hardy or Lebesgue space. Our results generalize to the weighted setting results obtained by Grafakos and Kalton  and recent work by the third author, Grafakos, Nakamura, and Sawano . As part of our proof we provide a finite atomic decomposition theorem for weighted Hardy spaces, which is interesting in its own right. As a consequence of our weighted results, we prove the corresponding estimates on variable Hardy spaces. Our main tool is a multilinear extrapolation theorem that generalizes a result of the first author and Naibo .
David Cruz-Uribe OFS. Kabe Moen. Hanh Van Nguyen. "The Boundedness of Multilinear Calderón-Zygmund Operators on Weighted and Variable Hardy Spaces." Publ. Mat. 63 (2) 679 - 713, 2019. https://doi.org/10.5565/PUBLMAT6321908