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 R-d, d >= 3, and related estimates for oscillatory integral operators. Moreover, for some larger classes of curves in Rd we obtain sharp uniform L-p -> L-q bounds with respect to affine arclength measure, thereby resolving a problem of Drury and Marshall.