Discrete Fourier restriction associated with Schrodinger equations

摘要

We present a novel proof on the discrete Fourier restriction. The proof recovers Bourgain's level set result for Strichartz estimates associated with Schrodinger equations on a torus. Some sharp estimates on L2(d+2)/d 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 L-2 (Z).