882 research outputs found
Convolution with measures on flat curves in low dimensions
We prove convolution estimates for affine arclength measure on certain flat
curves in dimensions 2, 3, and 4
Restriction of Fourier transforms to curves, II: Some classes with vanishing torsion
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.Comment: 26 pages, Final version to appear in the Journal of the Australian
Mathematical Societ
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 , , and related
estimates for oscillatory integral operators. Moreover, for some larger classes
of curves in we obtain sharp uniform bounds with
respect to affine arclength measure, thereby resolving a problem of Drury and
Marshall.Comment: Minor changes in the version to appear in American Journal of
Mathematic
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