{"title":"C- i的p范数，其中C是Cesàro算子","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":"{\"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}","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
摘要
对于Cesaro算子C，已知||C- i ||_2 = 1。我们证明| |我| | _4 < 3 ^(1/4)和| | C ^我| | _4 = 3。由Riesz-Thorin插值定理导出了p的中间值的边界。得到了下界的估计。
The ℓ_p-norm of C-I, where C is the Cesàro operator
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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