The Tomas–Stein inequality under the effect of symmetries

Rainer Mandel, D. O. Silva
{"title":"The Tomas–Stein inequality under the effect of symmetries","authors":"Rainer Mandel, D. O. Silva","doi":"10.5445/IR/1000134152","DOIUrl":null,"url":null,"abstract":"We prove new Fourier restriction estimates to the unit sphere $\\mathbb{S}^{d-1}$ on the class of $O(d−k) \\times O(k)$-symmetric functions, for every $d \\ge 4$ and $2 \\le k \\le d-2$. As an application, we establish the existence of maximizers for the endpoint Tomas–Stein inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp in the Tomas–Stein regime.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5445/IR/1000134152","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1

Abstract

We prove new Fourier restriction estimates to the unit sphere $\mathbb{S}^{d-1}$ on the class of $O(d−k) \times O(k)$-symmetric functions, for every $d \ge 4$ and $2 \le k \le d-2$. As an application, we establish the existence of maximizers for the endpoint Tomas–Stein inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp in the Tomas–Stein regime.
对称作用下的托马斯-斯坦不等式
我们证明了在$O(d−k) \times O(k)$对称函数类上,对于每一个$d \ge 4$和$2 \le k \le d-2$,单位球$\mathbb{S}^{d-1}$的新的傅里叶限制估计。作为一个应用,我们在该类中建立了端点Tomas-Stein不等式的极大值存在性。此外,我们构造的例子表明,在我们的估计中,勒贝格指数的范围在托马斯-斯坦政权中是尖锐的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信