Comptes Rendus
no. 1-2
Harmonic Analysis/Mathematical Analysis
Fourier restriction, polynomial curves and a geometric inequality
[Restrictions de Fourier et courbes polynomiales ; une inégalité géométrique]

Présenté par : Jean-Pierre Kahane

Spyridon Dendrinos1 ; James Wright2
1 Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
2 School of Mathematics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK
Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 45-48.

Le résultat que nous annonçons sur les restrictions de Fourier vaut pour des courbes polynomiales générales dans Rd. Il permet de contrôler la norme Lq de la transformée de Fourier relativement à la mesure d'arc affine (dont nous rappelons la définition) à la norme Lp 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.

We announce a Fourier restriction result for general polynomial curves in Rd. 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.11.032

Spyridon Dendrinos 1 ; James Wright 2

1 Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
2 School of Mathematics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK 
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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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