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

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, Nakam...

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Published in:Publicacions matemàtiques 2019, Vol.63 (2), p.679-713
Main Authors: Cruz-Uribe, David, Moen, Kabe, Van Nguyen, Hanh
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Moen, Kabe
Van Nguyen, Hanh
description 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].
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title The boundedness of multilinear Calderón-Zygmund operators on weighted and variable Hardy spaces
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