A variation norm Carleson theorem

Richard Oberlin; Andreas Seeger; Terence Tao; Christoph Thiele; James Wright

doi:10.4171/jems/307

JournalsjemsVol. 14, No. 2pp. 421–464

A variation norm Carleson theorem

Richard Oberlin
Louisiana State University, Baton Rouge, USA
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Andreas Seeger
University of Wisconsin, Madison, USA
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Terence Tao
University of California Los Angeles, United States
Christoph Thiele
Universität Bonn, Germany
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- zbMATH Open
James Wright
University of Edinburgh, UK
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Abstract

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

Richard Oberlin, Andreas Seeger, Terence Tao, 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