On the Restriction of the Fourier Transform to a Conical Surface

Abstract

Let r be the surface of a circular cone in R3.We show that if 1 < p < 4/3, 1/g = 3(1 -1/p) and / 6 LP(R3), then the Fourier transform of / belongs to Lq{T,da) for a certain natural measure a on I\ Following P. Tomas we also establish bounds for restrictions of Fourier transforms to conic annuli at the endpoint p = 4/3, with logarithmic growth of the bound as the thickness of the annulus tends to zero.

Locations

• Transactions of the American Mathematical Society - View - PDF