{"title":"The ℓ_p-norm of C-I, where C is the Cesàro operator","authors":"G. Jameson","doi":"10.7153/MIA-2021-24-38","DOIUrl":null,"url":null,"abstract":"For the Cesaro operator C, it is known that ||C-I||_2 = 1. Here we prove that ||C-I||_4 < 3^(1/4) and ||C^T-I||_4 = 3. Bounds for intermediate values of p are derived from the Riesz-Thorin interpolation theorem. An estimate for lower bounds is obtained.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"551-557"},"PeriodicalIF":0.9000,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Inequalities & Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/MIA-2021-24-38","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
For the Cesaro operator C, it is known that ||C-I||_2 = 1. Here we prove that ||C-I||_4 < 3^(1/4) and ||C^T-I||_4 = 3. Bounds for intermediate values of p are derived from the Riesz-Thorin interpolation theorem. An estimate for lower bounds is obtained.
期刊介绍：
''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.
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