A variation norm Carleson theorem

  • Terence Tao

    University of California Los Angeles, United States
  • Richard Oberlin

    Louisiana State University, Baton Rouge, USA
  • Andreas Seeger

    University of Wisconsin, Madison, USA
  • Christoph Thiele

    Universität Bonn, Germany
  • James Wright

    University of Edinburgh, UK


We strengthen the Carleson-Hunt theorem by proving estimates for the -variation of the partial sum operators for Fourier series and integrals, for . Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.

Cite this article

Terence Tao, Richard Oberlin, Andreas Seeger, Christoph Thiele, James Wright, A variation norm Carleson theorem. J. Eur. Math. Soc. 14 (2012), no. 2, pp. 421–464

DOI 10.4171/JEMS/307