Some remarks on the restriction of the Fourier transform to surfaces
For a class of kernels, we prove the Lp estimate for the exotic Riesz potential, with which a restriction theorem of the Fourier transform to surfaces of half the ambient dimension is proved. A simpler proof of Barcelo's result is given. We also find that it is possible to combine the Hausdorff-Young theorem with the Fefferman-Zygmund method to prove some optimal results on the restriction theorem.
Drury, S. W., and K. Guo. "Some remarks on the restriction of the Fourier transform to surfaces." In Mathematical Proceedings of the Cambridge Philosophical Society, vol. 113, no. 1, pp. 153-159. Cambridge University Press, 1993.
Mathematical Proceedings of the Cambridge Philosophical Society