Variational estimates for paraproducts

  • Yen Do

    Yale University, New Haven, USA
  • Camil Muscalu

    Cornell University, Ithaca, USA
  • Christoph Thiele

    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.

Cite this article

Yen Do, Camil Muscalu, Christoph Thiele, Variational estimates for paraproducts. Rev. Mat. Iberoam. 28 (2012), no. 3, pp. 857–878

DOI 10.4171/RMI/694