A sharp Schrödinger maximal estimate in R 2

Xiumin Du, Larry Guth, Xiaochun Li

Research output: Contribution to journalArticle

Abstract

We show that limt→0 e itΔ f(x) = f(x) almost everywhere for all f ∈ H s (R 2 ) provided that s > 1/3. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.

Original languageEnglish (US)
Pages (from-to)607-640
Number of pages34
JournalAnnals of Mathematics
Volume186
Issue number2
DOIs
StatePublished - Jan 1 2017

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Decoupling
Partitioning
Polynomial
Estimate
Polynomials

Keywords

  • Decoupling
  • Polynomial partitioning
  • Restriction
  • Schrodinger equation
  • Schrodinger maximal function

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

A sharp Schrödinger maximal estimate in R 2 . / Du, Xiumin; Guth, Larry; Li, Xiaochun.

In: Annals of Mathematics, Vol. 186, No. 2, 01.01.2017, p. 607-640.

Research output: Contribution to journalArticle

Du, Xiumin ; Guth, Larry ; Li, Xiaochun. / A sharp Schrödinger maximal estimate in R 2 In: Annals of Mathematics. 2017 ; Vol. 186, No. 2. pp. 607-640.
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