Restriction of Fourier transforms to curves and related oscillatoryintegrals

We prove sharp endpoint results for the Fourier restriction operator associated to nondegenerate curves in Rᵈ, d≥ 3, and related estimates for oscillatory integral operators. Moreover, for some larger classes of curves in Rᵈ we obtain sharp uniform Lᵖ→ Lq bounds with respect to affine arclength measure, thereby resolving a problem of Drury and Marshall.