Revista Matemática Iberoamericana

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Volume 28, Issue 3, 2012, pp. 857–878
DOI: 10.4171/RMI/694

Published online: 2012-07-16

Variational estimates for paraproducts

Yen Do[1], Camil Muscalu[2] and Christoph Thiele[3]

(1) Yale University, New Haven, USA
(2) Cornell University, Ithaca, USA
(3) Universität Bonn, Germany

We generalize a family of variation norm estimates (Theorem 1.1) of Lépingle with endpoint estimates of Bourgain and Pisier–Xu to a family of variational estimates for paraproducts (Theorem 1.2), both in the discrete and the continuous setting. This expands on work of Friz and Victoir, our focus being on the continuous case and an expanded range of variation exponents.

Keywords: Littlewood–Paley theory, paraproduct, variation norm

Do Yen, Muscalu Camil, Thiele Christoph: Variational estimates for paraproducts. Rev. Mat. Iberoam. 28 (2012), 857-878. doi: 10.4171/RMI/694