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. 421–464DOI 10.4171/JEMS/307