### 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 language | English (US) |
---|---|

Pages (from-to) | 607-640 |

Number of pages | 34 |

Journal | Annals of Mathematics |

Volume | 186 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

^{2}

*Annals of Mathematics*,

*186*(2), 607-640. https://doi.org/10.4007/annals.2017.186.2.5

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

Research output: Contribution to journal › Article

^{2}'

*Annals of Mathematics*, vol. 186, no. 2, pp. 607-640. https://doi.org/10.4007/annals.2017.186.2.5

^{2}Annals of Mathematics. 2017 Jan 1;186(2):607-640. https://doi.org/10.4007/annals.2017.186.2.5

}

TY - JOUR

T1 - A sharp Schrödinger maximal estimate in R 2

AU - Du, Xiumin

AU - Guth, Larry

AU - Li, Xiaochun

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Decoupling

KW - Polynomial partitioning

KW - Restriction

KW - Schrodinger equation

KW - Schrodinger maximal function

UR - http://www.scopus.com/inward/record.url?scp=85027224135&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027224135&partnerID=8YFLogxK

U2 - 10.4007/annals.2017.186.2.5

DO - 10.4007/annals.2017.186.2.5

M3 - Article

VL - 186

SP - 607

EP - 640

JO - Annals of Mathematics

T2 - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 2

ER -