The author states the results of his paper in the abstract of the paper. For smooth curves
with certain curvature properties he shows that the composition of the Fourier transform in
followed by restriction to
defines a bounded operator from
for certain p and q. The curvature hypotheses are the weakest under which this can hold, and p is optimal for a range of q. In the proofs the problem is reduced to the estimation of certain multilinear operators generalizing fractional integrals, and they are treated by means of rearrangement inequalities and interpolation between simple endpoint estimates.