{"title":"关于拉普拉斯变换的算子范数的注释","authors":"T. Peachey","doi":"10.1080/10652469.2022.2026351","DOIUrl":null,"url":null,"abstract":"Determination of the operator norm for the Laplace transformation, when operating on Lebesgue spaces, is a long unsolved problem. Recently Setterqvist gave an improved bound to that norm. This note shows how his result relates to a more general theorem, which also gives a related reverse inequality, and some other results of Hardy, Littlewood and Pólya.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"33 1","pages":"711 - 714"},"PeriodicalIF":0.7000,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on the operator norm of the Laplace transformation\",\"authors\":\"T. Peachey\",\"doi\":\"10.1080/10652469.2022.2026351\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Determination of the operator norm for the Laplace transformation, when operating on Lebesgue spaces, is a long unsolved problem. Recently Setterqvist gave an improved bound to that norm. This note shows how his result relates to a more general theorem, which also gives a related reverse inequality, and some other results of Hardy, Littlewood and Pólya.\",\"PeriodicalId\":54972,\"journal\":{\"name\":\"Integral Transforms and Special Functions\",\"volume\":\"33 1\",\"pages\":\"711 - 714\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Integral Transforms and Special Functions\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/10652469.2022.2026351\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Integral Transforms and Special Functions","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10652469.2022.2026351","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A note on the operator norm of the Laplace transformation
Determination of the operator norm for the Laplace transformation, when operating on Lebesgue spaces, is a long unsolved problem. Recently Setterqvist gave an improved bound to that norm. This note shows how his result relates to a more general theorem, which also gives a related reverse inequality, and some other results of Hardy, Littlewood and Pólya.
期刊介绍：
Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.
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