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Fourier restriction to polynomial curves I: a geometric inequality
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 132, Number 4, August 2010
- pp. 1031-1076
- 10.1353/ajm.0.0127
- Article
- Additional Information
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.