Fourier restriction to polynomial curves I: a geometric inequality

Spyridon Dendrinos, James Wright

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Abstract

We prove a Fourier restriction result for general polynomial curves in R-d. Measuring the Fourier restriction with respect to the affine arclength measure of the curve. we obtain a universal estimate for the class of all polynomial curves of bounded degree. Our method relies on establishing a geometric inequality for general polynomial curves which is of interest in its own right. Applications of this geometric inequality to other problems in euclidean harmonic analysis have recently been established.

Original languageEnglish
Pages (from-to)1031-1076
Number of pages46
JournalAmerican Journal of Mathematics
Volume132
Issue number4
DOIs
Publication statusPublished - Aug 2010

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