Daniel M. Oberlin

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

RESTRICTION OF FOURIER TRANSFORMS TO CURVES II: SOME CLASSES WITH VANISHING TORSION

{\Bbb R}^d

Two endpoint bounds for generalized Radon transforms in the plane

,

Fourier restriction for affine arclength measures in the plane

d\ge 3

Restricted Radon Transforms and Projections of Planar Sets

, and related estimates for oscillatory integral operators. Moreover, for some larger classes of curves in

Some convolution inequalities and their applications

{\Bbb R}^d

Two estimates for curves in the plane

we obtain sharp uniform

An Estimate For a Restricted X-Ray Transform

L^p\to L^q

M p(G)≠M q(G) (p −1+q −=1)

bounds with respect to affine arclength measure, thereby resolving a problem of Drury and Marshall.

L p -L q estimates off the line of duality

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.