The boundedness of multilinear Calderón-Zygmund operators on weighted and variable Hardy spaces

Cruz-Uribe, David ^[1] ; Moen, Kabe ^[1] ; Van Nguyen, Hanh ^[1]
1. [1] University of Alabama. Department of Mathematics
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 63, Nº 2, 2019, págs. 679-713
Idioma: inglés
DOI: 10.5565/PUBLMAT6321908
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Resumen
- We establish the boundedness of the multilinear Calderon{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 [18] and recent work by the third author, Grafakos, Nakamura, and Sawano [20]. 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 [10].