Revista Matemática Iberoamericana

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Volume 30, Issue 4, 2014, pp. 1281–1300
DOI: 10.4171/RMI/815

Published online: 2014-12-15

Discrete Fourier restriction associated with Schrödinger equations

Yi Hu[1] and Xiaochun Li[2]

(1) Georgia Southern University, Statesboro, USA
(2) University of Illinois at Urbana-Champaign, USA

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 $L^{{2(d+2)}/{d}}$ 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 $L^2(\mathbb Z)$.

Keywords: Discrete Fourier restriction, Strichartz estimates, exponential sums, multilinear maximal function

Hu Yi, Li Xiaochun: Discrete Fourier restriction associated with Schrödinger equations. Rev. Mat. Iberoam. 30 (2014), 1281-1300. doi: 10.4171/RMI/815