Fourier restriction, polynomial curves and a geometric inequality

Dendrinos, Spyridon; Wright, James

doi:10.1016/j.crma.2007.11.032

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

Dendrinos, Spyridon ¹ ; Wright, James 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

Comptes Rendus. Mathématique, Tome 346 (2008) no. 1-2, pp. 45-48.

Résumé
Abstract

Le résultat que nous annonçons sur les restrictions de Fourier vaut pour des courbes polynomiales générales dans $R^{d}$ . Il permet de contrôler la norme $L^{q}$ de la transformée de Fourier relativement à la mesure d'arc affine (dont nous rappelons la définition) à la norme $L^{p}$ 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 $R^{d}$ . 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 : 2007-06-19
Accepté le : 2007-11-22
Publié le : 2008-01-01

DOI : 10.1016/j.crma.2007.11.032

Affiliations des auteurs :

Dendrinos, Spyridon ¹ ; Wright, James ²

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Dendrinos, Spyridon; Wright, James. Fourier restriction, polynomial curves and a geometric inequality. Comptes Rendus. Mathématique, Tome 346 (2008) no. 1-2, pp. 45-48. doi : 10.1016/j.crma.2007.11.032. http://www.numdam.org/articles/10.1016/j.crma.2007.11.032/

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