We announce a Fourier restriction result for general polynomial curves in . Measuring the Fourier restriction with respect to the affine arclength measure of the curve, we obtain a universal bound 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. There are applications of this geometric inequality to other problems in euclidean harmonic analysis.
Le résultat que nous annonçons sur les restrictions de Fourier vaut pour des courbes polynomiales générales dans . Il permet de contrôler la norme de la transformée de Fourier relativement à la mesure d'arc affine (dont nous rappelons la définition) à la norme de la fonction, pour des p et q convenables. La borne est universelle pour toutes les courbes polynomiales de degré donné. Notre méthode repose sur une inégalité géométrique concernant les courbes polynomiales qui est intéressante en elle même, et s'applique à d'autres problèmes d'analyse harmonique euclidienne.
Accepted:
Published online:
Spyridon Dendrinos 1; James Wright 2
@article{CRMATH_2008__346_1-2_45_0,
author = {Spyridon Dendrinos and James Wright},
title = {Fourier restriction, polynomial curves and a geometric inequality},
journal = {Comptes Rendus. Math\'ematique},
pages = {45--48},
publisher = {Elsevier},
volume = {346},
number = {1-2},
year = {2008},
doi = {10.1016/j.crma.2007.11.032},
language = {en},
}
Spyridon Dendrinos; James Wright. Fourier restriction, polynomial curves and a geometric inequality. Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 45-48. doi : 10.1016/j.crma.2007.11.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.11.032/
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