Restriction of Fourier transforms to curves, II: Some classes with vanishing torsion

Details Restriction of Fourier transforms to curves, II: Some classes with vanishing torsion Restriction of Fourier transforms to curves, II: Some classes with vanishing torsion

2007-03-02

arxiv.org/abs/math/0703068v2

Journal of the Australian Mathematical Society, 85 (2008), 1-28.

Mathematics

Classical Analysis and ODEs

26 pages, Final version to appear in the Journal of the Australian Mathematical Society

Scientific paper

We consider the Fourier restriction operators associated to certain
degenerate curves in R^d for which the highest torsion vanishes. We prove
estimates with respect to affine arclength and with respect to the Euclidean
arclength measure on the curve. The estimates have certain uniform features,
and the affine arclength results cover families of flat curves.

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