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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.
Peter A. Tomas (Wed,) studied this question.