Jong-Guk Bak

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

,

Estimates for an oscillatory integral operator related to restriction to space curves

d\ge 3

Extensions of the Stein–Tomas Theorem

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

Restriction of Fourier transforms to curves: An endpoint estimate with affine arclength measure

{\Bbb R}^d

FOURIER TRANSFORMS OF SURFACE AREA MEASURE ON CONVEX SURFACES IN R3

we obtain sharp uniform

Convolution of a measure with itself and a restriction theorem

L^p\to L^q

Restriction of the Fourier transform to some complex curves

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

Restriction of the Fourier transform to a quadratic surface in n

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.