LOCAL MAXIMIZERS OF ADJOINT FOURIER RESTRICTION ESTIMATES FOR THE CONE, PARABOLOID AND SPHERE

被引：8

作者：

Goncalves, Felipe ^{[1
]}

Negro, Giuseppe ^{[2
]}

机构：

[1] Univ Bonn, Hausdorff Ctr Math, Bonn, Germany

[2] Inst Super Tecn, Dept Matemat, Lisbon, Portugal

来源：

ANALYSIS & PDE | 2022年 / 15卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Fourier extension; Fourier restriction; Schr?dinger equation; wave equation; Strichartz estimates; sharp inequality; local maximizer; cone; paraboloid; WAVE-EQUATION; INEQUALITY; INTEGRALS;

D O I：

10.2140/apde.2022.15.1097

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that, possibly after a compactification of spacetime, constant functions are local maximizers of the Tomas-Stein adjoint Fourier restriction inequality for the cone and paraboloid in every dimension, and for the sphere in dimension up to 60. For the cone and paraboloid we work from the PDE framework, which enables the use of the Penrose and the Lens transformations, which map the conjectured optimal functions into constants.

引用

页码：1096 / 1130

页数：35

共 23 条

[1]

[Anonymous], 2009, New York J. Math.

[2]

[Anonymous], 2006, CBMS Regional Series in Mathematics

[3]

[Anonymous], 2007, Table of Integrals, Series, and Products

[4] Mass concentration phenomena for the L2-critical nonlinear Schrodinger equation [J].