JournalsjemsVol. 14, No. 2pp. 421–464

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
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Abstract

We strengthen the Carleson-Hunt theorem by proving LpL^p estimates for the rr-variation of the partial sum operators for Fourier series and integrals, for r>max{p,2}r>\max\{p',2\}. 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