Restriction of Fourier transforms to curves and related oscillatory integrals

Details Restriction of Fourier transforms to curves and related oscillatory integrals Restriction of Fourier transforms to curves and related oscillatory integrals

2006-12-24

arxiv.org/abs/math/0612752v2

American Journal of Mathematics, 131, no.2 (2009), 277-311.

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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.

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