Fourier transform, $L^2$ restriction theorem, and scaling

Alex Iosevich

paper

Fourier transform, $L^{2}$ restriction theorem, and scaling

arXiv:math/0104097

Abstract

We show, using a Knapp-type homogeneity argument, that the $(L^{p}, L^{2})$ restriction theorem implies a growth condition on the hypersurface in question. We further use this result to show that the optimal $(L^{p}, L^{2})$ restriction theorem implies the sharp isotropic decay rate for the Fourier transform of the Lebesgue measure carried by compact convex finite hypersurfaces.

Fourier transform, L2 restriction theorem, and scaling

Abstract

Fourier transform, $L^{2}$ restriction theorem, and scaling