Abstract

We prove a Fourier restriction result for general polynomial curves in ${\Bbb R}^d$. 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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1031-1076
Launched on MUSE
2010-07-31
Open Access
No
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