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

Keywords

Discrete Fourier restriction
Exponential sums
Multilinear maximal function
Strichartz estimates

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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",

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AU - Hu, Yi

AU - Li, Xiaochun

N1 - Publisher Copyright: © European Mathematical Society.

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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

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U2 - 10.4171/rmi/815

DO - 10.4171/rmi/815

M3 - Article

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EP - 1300

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 4

ER -

Discrete Fourier restriction associated with Schrödinger equations

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Keywords

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