A variation norm Carleson theorem

Details A variation norm Carleson theorem A variation norm Carleson theorem

2009-10-08

arxiv.org/abs/0910.1555v2

Mathematics

Classical Analysis and ODEs

41 pages

Scientific paper

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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