Sharp estimates for oscillatory integral operators via polynomial partitioning

被引：40

作者：

Guth, Larry ^{[1
]}

Hickman, Jonathan ^{[2
,3
]}

Iliopoulou, Marina ^{[4
,5
]}

机构：

[1] MIT, Dept Math, 182 Mem Dr, Cambridge, MA 02139 USA

[2] Univ Chicago, Dept Math, Eckhart Hall Room 414,5734 S Univ Ave, Chicago, IL 60637 USA

[3] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland

[4] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[5] Univ Kent, Sch Math Stat & Actuarial Sci, Sibson Bldg,Room 262,Parkwood Rd, Canterbury CT2 7FS, Kent, England

来源：

ACTA MATHEMATICA | 2019年 / 223卷 / 02期

基金：

美国国家科学基金会;

关键词：

BOCHNER-RIESZ; RESTRICTION; CONJECTURE; BOUNDS; SETS;

D O I：

10.4310/ACTA.2019.v223.n2.a2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The sharp range of Lp-estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments. The main result implies improved bounds for the Bochner–Riesz conjecture in dimensions (Formula Presented). © 2019 by Institut Mittag-Leffler. All rights reserved.

引用

页码：251 / 376

页数：126

共 39 条

[1]

[Anonymous], 1970, SINGULAR INTEGRALS D

[2] Multivariate simultaneous approximation [J].