BOUNDS ON OSCILLATORY INTEGRAL OPERATORS BASED ON MULTILINEAR ESTIMATES

被引：196

作者：

Bourgain, Jean ^{[1
]}

Guth, Larry ^{[2
]}

机构：

[1] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2011年 / 21卷 / 06期

基金：

美国国家科学基金会;

关键词：

Restriction; oscillatory integral operator; Kakeya; RESTRICTION;

D O I：

10.1007/s00039-011-0140-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply the Bennett-Carbery-Tao multilinear restriction estimate in order to bound restriction operators and more general oscillatory integral operators. We get improved L-p estimates in the Stein restriction problem for dimension at least 5 and a small improvement in dimension 3. We prove similar estimates for Hormander-type oscillatory integral operators when the quadratic term in the phase function is positive definite, getting improvements in dimension at least 5. We also prove estimates for Hormander-type oscillatory integral operators in even dimensions. These last oscillatory estimates are related to improved bounds on the dimensions of curved Kakeya sets in even dimensions.

引用

页码：1239 / 1295

页数：57

共 19 条

[1]

[Anonymous], P S PURE MATH

[2] On the multilinear restriction and Kakeya conjectures [J].