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A variation norm Carleson theorem
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A variation norm Carleson theorem
classification
math.CA
keywords
theoremvariationfouriernormappendicesapplicationscarlesoncarleson-hunt
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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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