Fourier restriction to polynomial curves I: a geometric inequality

Dendrinos, S. and Wright, J. (2010) Fourier restriction to polynomial curves I: a geometric inequality. American Journal of Mathematics, 132(2), pp. 1031-1076. (doi: 10.1353/ajm.0.0127)

Abstract

We prove 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 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.

• Item Type: Articles
• Additional Information: Reprinted with permission of The Johns Hopkins University Press.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Dendrinos, Dr Spyridon
• Authors: Dendrinos, S., and Wright, J.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Research Group: Analysis
• Journal Name: American Journal of Mathematics
• Journal Abbr.: Amer. J. Math.
• Publisher: John Hopkins University Press
• ISSN: 0002-9327
• ISSN (Online): 1080-6377
• Copyright Holders: Copyright © 2010 John Hopkins University Press
• First Published: First published in American Journal of Mathematics 132(2)
• Publisher Policy: Reproduced with the permission of the publisher.