{"title":"Sharp Bernstein Inequalities on Simplex","authors":"Yan Ge, Yuan Xu","doi":"10.1007/s00365-024-09680-6","DOIUrl":null,"url":null,"abstract":"<p>We prove several new families of Bernstein inequalities of two types on the simplex. The first type consists of inequalities in <span>\\(L^2\\)</span> norm for the Jacobi weight, some of which are sharp, and they are established via the spectral operator that has orthogonal polynomials as eigenfunctions. The second type consists of inequalities in <span>\\(L^p\\)</span> norm for doubling weight on the simplex. The first type is not necessarily a special case of the second type when <span>\\(d \\ge 3\\)</span>.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00365-024-09680-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove several new families of Bernstein inequalities of two types on the simplex. The first type consists of inequalities in \(L^2\) norm for the Jacobi weight, some of which are sharp, and they are established via the spectral operator that has orthogonal polynomials as eigenfunctions. The second type consists of inequalities in \(L^p\) norm for doubling weight on the simplex. The first type is not necessarily a special case of the second type when \(d \ge 3\).
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
