  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.
