We present a novel proof on the discrete Fourier restriction. The proof recovers Bourgain's level set result for Strichartz estimates associated with Schrödinger equations on a torus. Some sharp estimates on norms of certain exponential sums in higher dimensional cases are established. As an application, we show that some discrete multilinear maximal functions are bounded on .
Cite this article
Yi Hu, Xiaochun Li, Discrete Fourier restriction associated with Schrödinger equations. Rev. Mat. Iberoam. 30 (2014), no. 4, pp. 1281–1300DOI 10.4171/RMI/815