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Restriction of Fourier transforms to curves and related oscillatory integrals


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.