Open AccessA variation norm Carleson theorem
Author(s) -
Richard Oberlin,
Andreas Seeger,
Terence Tao,
Christoph Thiele,
James Wright
Publication year - 2012
Publication title -
journal of the european mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.549
H-Index - 64
eISSN - 1435-9863
pISSN - 1435-9855
DOI - 10.4171/jems/307
Subject(s) - mathematics , norm (philosophy) , variation (astronomy) , pure mathematics , physics , astrophysics , political science , law
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, avariation norm Menshov-Paley-Zygmund theorem, and applications to nonlinearFourier transforms and ergodic theory.
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