A sharp Schrödinger maximal estimate in R2

Xiumin Du; Larry Guth; Xiaochun Li

doi:10.4007/annals.2017.186.2.5

A sharp Schrödinger maximal estimate in R²

Xiumin Du, Larry Guth, Xiaochun Li

Mathematics

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

Abstract

We show that limt→0 e^itΔf(x) = f(x) almost everywhere for all f ∈ H^s(R²) provided that s > 1/3. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.

Original language	English (US)
Pages (from-to)	607-640
Number of pages	34
Journal	Annals of Mathematics
Volume	186
Issue number	2
DOIs	https://doi.org/10.4007/annals.2017.186.2.5
State	Published - 2017

Keywords

Decoupling
Polynomial partitioning
Restriction
Schrodinger equation
Schrodinger maximal function

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Online availability

10.4007/annals.2017.186.2.5

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Cite this

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title = "A sharp Schr{\"o}dinger maximal estimate in R2",

abstract = "We show that limt→0 eitΔf(x) = f(x) almost everywhere for all f ∈ Hs(R2) provided that s > 1/3. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.",

keywords = "Decoupling, Polynomial partitioning, Restriction, Schrodinger equation, Schrodinger maximal function",

author = "Xiumin Du and Larry Guth and Xiaochun Li",

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