{"title":"单调极值函数与加权希尔伯特不等式","authors":"E. Carneiro, Friedrich Littmann","doi":"10.4171/pm/2109","DOIUrl":null,"url":null,"abstract":"In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the (non-sharp) weighted Hilbert-Montgomery-Vaughan inequality.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Monotone extremal functions and the weighted Hilbert’s inequality\",\"authors\":\"E. Carneiro, Friedrich Littmann\",\"doi\":\"10.4171/pm/2109\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the (non-sharp) weighted Hilbert-Montgomery-Vaughan inequality.\",\"PeriodicalId\":51269,\"journal\":{\"name\":\"Portugaliae Mathematica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Portugaliae Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/pm/2109\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Portugaliae Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/pm/2109","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Monotone extremal functions and the weighted Hilbert’s inequality
In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the (non-sharp) weighted Hilbert-Montgomery-Vaughan inequality.
期刊介绍：
Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.
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