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arXiv · 0910.1555

A variation norm Carleson theorem

Richard Oberlin·Andreas Seeger·Terence Tao·Christoph Thiele·James Wright
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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 $p>\max\{r',2\}$. Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.

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Richard Oberlin, Andreas Seeger, Terence Tao, Christoph Thiele, James Wright. 2010-08-25. A variation norm Carleson theorem. https://arxiv.org/abs/0910.1555

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