A restriction theorem for the Fourier transform

Let be a Schwartz function on R n , and let (0) denote the restriction of the Fourier transform of to the unit sphere S n ~x in R n . We prove THEOREM. Iff is in L p (R n ) for some p with 1 < p < 2(n +1)/( + 3), then 5 s n-i)\ 2 de<c p \\\ 2 p .