Restriction of Fourier transforms to curves and related oscillatory integrals

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

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Bibliographic Details
Main Authors Bak, Jong-Guk, Oberlin, Daniel M, Seeger, Andreas
Format Journal Article
LanguageEnglish
Published 24.12.2006
Subjects
Mathematics - Classical Analysis and ODEs
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Summary:American Journal of Mathematics, 131, no.2 (2009), 277-311. 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.
DOI:10.48550/arxiv.math/0612752