Revista Matemática Iberoamericana
In this paper, we present a different proof on the discrete Fourier restriction. The proof recovers Bourgain’s level set result on Strichartz estimates associated with Schrödinger equations on torus. Some sharp estimates on L 2(d+2) d norm 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).
Hu, Yi, Xiaochun Li.
"Discrete Fourier Restriction Associated with Schrödinger Equations."
Revista Matemática Iberoamericana, 30 (4): 1281-1300.
doi: 10.4171/RMI/815 source: http://arxiv.org/abs/1108.5164