Restriction of Fourier transforms to curves and related oscillatory integrals

Abstract

We prove sharp endpoint results for the Fourier restriction operator associated to nondegenerate curves in ${\mathbb{R}}^d$, $d\ge 3$, and related estimates for oscillatory integral operators. Moreover, for some larger classes of curves in ${\mathbb{R}}^d$ we obtain sharp uniform $L^p\to L^q$ bounds with respect to affine arclength measure, thereby resolving a problem of Drury and Marshall.

Minor changes in the version to appear in American Journal of Mathematics

Cited by in corpus (2)

• Universal L^p improving for averages along polynomial curves in low dimensions
• Restriction of Fourier transforms to curves, II: Some classes with vanishing torsion