{"title":"单片超球面上傅里叶限制不等式的极值存在性","authors":"René Quilodrán","doi":"10.1007/s00041-024-10090-2","DOIUrl":null,"url":null,"abstract":"<p>We prove the existence of functions that extremize the endpoint <span>\\(L^2\\)</span> to <span>\\(L^4\\)</span> adjoint Fourier restriction inequality on the one-sheeted hyperboloid in Euclidean space <span>\\(\\mathbb {R}^4\\)</span> and that, taking symmetries into consideration, any extremizing sequence has a subsequence that converges to an extremizer.\n</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence of Extremals for a Fourier Restriction Inequality on the One-Sheeted Hyperboloid\",\"authors\":\"René Quilodrán\",\"doi\":\"10.1007/s00041-024-10090-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove the existence of functions that extremize the endpoint <span>\\\\(L^2\\\\)</span> to <span>\\\\(L^4\\\\)</span> adjoint Fourier restriction inequality on the one-sheeted hyperboloid in Euclidean space <span>\\\\(\\\\mathbb {R}^4\\\\)</span> and that, taking symmetries into consideration, any extremizing sequence has a subsequence that converges to an extremizer.\\n</p>\",\"PeriodicalId\":15993,\"journal\":{\"name\":\"Journal of Fourier Analysis and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fourier Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00041-024-10090-2\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fourier Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00041-024-10090-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Existence of Extremals for a Fourier Restriction Inequality on the One-Sheeted Hyperboloid
We prove the existence of functions that extremize the endpoint \(L^2\) to \(L^4\) adjoint Fourier restriction inequality on the one-sheeted hyperboloid in Euclidean space \(\mathbb {R}^4\) and that, taking symmetries into consideration, any extremizing sequence has a subsequence that converges to an extremizer.
期刊介绍：
The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics.
TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers.
Areas of applications include the following:
antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications
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