{"title":"实域上可微函数$$$\\|x\\|_{p，\\delta} = \\sup \\bigl\\{\\|x\\|_{L_p[a,b]} \\冒号a,b\\in \\mathbb{R}， b-a\\leqslant \\delta \\bigr\\}$$$的各种度量不等式","authors":"V. Kofanov","doi":"10.15421/241806","DOIUrl":null,"url":null,"abstract":"We prove sharp inequalities of various metrics for the norms $$$\\| x \\|_{p, \\delta}$$$ of differentiable functions defined on the real line, trigonometric polynomials and periodic splines.","PeriodicalId":339757,"journal":{"name":"Dnipro University Mathematics Bulletin","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inequalities of various metrics for the norms $$$\\\\|x\\\\|_{p,\\\\delta} = \\\\sup \\\\bigl\\\\{ \\\\| x \\\\|_{L_p[a,b]} \\\\colon a,b\\\\in \\\\mathbb{R}, b-a\\\\leqslant \\\\delta \\\\bigr\\\\}$$$ of differentiable functions on the real domain\",\"authors\":\"V. Kofanov\",\"doi\":\"10.15421/241806\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove sharp inequalities of various metrics for the norms $$$\\\\| x \\\\|_{p, \\\\delta}$$$ of differentiable functions defined on the real line, trigonometric polynomials and periodic splines.\",\"PeriodicalId\":339757,\"journal\":{\"name\":\"Dnipro University Mathematics Bulletin\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dnipro University Mathematics Bulletin\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15421/241806\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dnipro University Mathematics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15421/241806","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们证明了实线、三角多项式和周期样条上定义的可微函数的范数$$$\ \ x \ \ _{p， \delta}$$$ $的各种度量的尖锐不等式。
Inequalities of various metrics for the norms $$$\|x\|_{p,\delta} = \sup \bigl\{ \| x \|_{L_p[a,b]} \colon a,b\in \mathbb{R}, b-a\leqslant \delta \bigr\}$$$ of differentiable functions on the real domain
We prove sharp inequalities of various metrics for the norms $$$\| x \|_{p, \delta}$$$ of differentiable functions defined on the real line, trigonometric polynomials and periodic splines.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
