A variation norm Carleson theorem

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

doi:10.4171/JEMS/307

A variation norm Carleson theorem

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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We strengthen the Carleson-Hunt theorem by proving Lp 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.

Original language	English
Article number	14
Pages (from-to)	421-464
Number of pages	43
Journal	Journal of the European Mathematical Society
Volume	14
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/307
Publication status	Published - 2012

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10.4171/JEMS/307

A VARIATION NORM CARLESON THEOREMAccepted author manuscript, 834 KB

http://www.maths.ed.ac.uk/~wright/papers

Cite this

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title = "A variation norm Carleson theorem",

abstract = "We strengthen the Carleson-Hunt theorem by proving Lp 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.",

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AU - Oberlin, Richard

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AB - We strengthen the Carleson-Hunt theorem by proving Lp 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.

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JO - Journal of the European Mathematical Society

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ER -

A variation norm Carleson theorem

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Degenerate Oscillatory Integral Operators

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A variation norm Carleson theorem

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Degenerate Oscillatory Integral Operators

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