# A variation norm Carleson theorem

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

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 2, page 421-464
- ISSN: 1435-9855

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topOberlin, Richard, et al. "A variation norm Carleson theorem." Journal of the European Mathematical Society 014.2 (2012): 421-464. <http://eudml.org/doc/277451>.

@article{Oberlin2012,

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> \texttt \{max\}\lbrace p^\{\prime \},2\rbrace $. Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.},

author = {Oberlin, Richard, Seeger, Andreas, Tao, Terence, Thiele, Christoph, Wright, James},

journal = {Journal of the European Mathematical Society},

keywords = {Fourier series; variation norm; Carleson theorem; Fourier series; variation norm; Carleson theorem},

language = {eng},

number = {2},

pages = {421-464},

publisher = {European Mathematical Society Publishing House},

title = {A variation norm Carleson theorem},

url = {http://eudml.org/doc/277451},

volume = {014},

year = {2012},

}

TY - JOUR

AU - Oberlin, Richard

AU - Seeger, Andreas

AU - Tao, Terence

AU - Thiele, Christoph

AU - Wright, James

TI - A variation norm Carleson theorem

JO - Journal of the European Mathematical Society

PY - 2012

PB - European Mathematical Society Publishing House

VL - 014

IS - 2

SP - 421

EP - 464

AB - 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> \texttt {max}\lbrace p^{\prime },2\rbrace $. Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.

LA - eng

KW - Fourier series; variation norm; Carleson theorem; Fourier series; variation norm; Carleson theorem

UR - http://eudml.org/doc/277451

ER -

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