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The Boundedness of Multilinear Calderón-Zygmund Operators on Weighted and Variable Hardy Spaces

David Cruz-Uribe, OFS, Kabe Moen, and Hanh Van Nguyen

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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 [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].

Article information

Publ. Mat., Volume 63, Number 2 (2019), 679-713.

Received: 16 November 2017
Revised: 6 March 2018
First available in Project Euclid: 28 June 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B25: Maximal functions, Littlewood-Paley theory 42B30: $H^p$-spaces 42B35: Function spaces arising in harmonic analysis

Muckenhoupt weights weighted Hardy spaces variable Hardy spaces multilinear Calderón-Zygmund operators singular integrals


Cruz-Uribe, David; Moen, Kabe; Van Nguyen, Hanh. The Boundedness of Multilinear Calderón-Zygmund Operators on Weighted and Variable Hardy Spaces. Publ. Mat. 63 (2019), no. 2, 679--713. doi:10.5565/PUBLMAT6321908.

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