- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
30
2014
4
Discrete Fourier restriction associated with Schrödinger equations
Yi
Hu
Georgia Southern University, STATESBORO, UNITED STATES
Xiaochun
Li
University of Illinois at Urbana-Champaign, URBANA, UNITED STATES
Discrete Fourier restriction, Strichartz estimates, exponential sums, multilinear maximal function
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 $L^2(\mathbb Z)$.
Fourier analysis
Number theory
1281
1300
10.4171/RMI/815
http://www.ems-ph.org/doi/10.4171/RMI/815