Discrete Fourier restriction associated with Schrödinger equations

Yi Hu; Xiaochun Li

doi:10.4171/rmi/815

Discrete Fourier restriction associated with Schrödinger equations

Yi Hu, Xiaochun Li

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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 L²(Z).

Original language	English
Pages (from-to)	1281-1300
Number of pages	20
Journal	Revista Matematica Iberoamericana
Volume	30
Issue number	4
DOIs	https://doi.org/10.4171/rmi/815
State	Published - 2014

Scopus Subject Areas

General Mathematics

Keywords

Discrete Fourier restriction
Exponential sums
Multilinear maximal function
Strichartz estimates

Access to Document

10.4171/rmi/815

Cite this

@article{ca42e89865a644419c3fe36f209201d5,

title = "Discrete Fourier restriction associated with Schr{\"o}dinger equations",

abstract = "We present a novel proof on the discrete Fourier restriction. The proof recovers Bourgain's level set result for Strichartz estimates associated with Schr{\"o}dinger 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 L2(Z).",

keywords = "Discrete Fourier restriction, Exponential sums, Multilinear maximal function, Strichartz estimates",

author = "Yi Hu and Xiaochun Li",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2014",

doi = "10.4171/rmi/815",

language = "English",

volume = "30",

pages = "1281--1300",

journal = "Revista Matematica Iberoamericana",

issn = "0213-2230",

publisher = "Universidad Autonoma de Madrid",

number = "4",

}

TY - JOUR

T1 - Discrete Fourier restriction associated with Schrödinger equations

AU - Hu, Yi

AU - Li, Xiaochun

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2014

Y1 - 2014

N2 - 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 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 L2(Z).

AB - 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 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 L2(Z).

KW - Discrete Fourier restriction

KW - Exponential sums

KW - Multilinear maximal function

KW - Strichartz estimates

UR - https://www.scopus.com/pages/publications/84919467431

U2 - 10.4171/rmi/815

DO - 10.4171/rmi/815

M3 - Article

SN - 0213-2230

VL - 30

SP - 1281

EP - 1300

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 4

ER -

Discrete Fourier restriction associated with Schrödinger equations

Abstract

Scopus Subject Areas

Keywords

Access to Document

Other files and links

Fingerprint

Cite this