Analyticity of extremizers to the Airy-Strichartz inequality

被引：14

作者：

Hundertmark, Dirk ^{[1
]}

Shao, Shuanglin ^{[2
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Univ Minnesota, Inst Math & Applicat, Minneapolis, MN 55455 USA

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2012年 / 44卷

基金：

美国国家科学基金会;

关键词：

CONCENTRATION-COMPACTNESS PRINCIPLE; LINEAR PROFILE DECOMPOSITION; EXISTENCE; APPROXIMATION; MAXIMIZERS; CALCULUS; EQUATION;

D O I：

10.1112/blms/bdr098

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that there exists an extremal function to the Airy-Strichartz inequality using the linear profile decomposition. Furthermore we show that, if f is an extremizer, then f is extremely fast decaying in Fourier space and so f can be extended to be an entire function on the whole complex domain. The rapid decay of the Fourier transform of extremizers is established with a bootstrap argument which relies on a refined bilinear Airy-Strichartz estimate and a weighted Strichartz inequality.

引用

页码：336 / 352

页数：17

共 37 条

[1] High frequency approximation of solutions to critical nonlinear wave equations [J].