Restriction of Fourier transforms to curves and related oscillatory integrals

Jong-Guk Bak, Daniel M. Oberlin, Andreas Seeger

Published 2006-12-24, updated 2008-06-04Version 2

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