{"title":"齐次锥中的hilbert型不等式","authors":"G. Garrigós, C. Nana","doi":"10.4171/RLM/916","DOIUrl":null,"url":null,"abstract":"We prove L-L bounds for the class of Hilbert-type operators associated with generalized powers Q in a homogeneous cone Ω. Our results extend and slightly improve earlier work from [10], where the problem was considered for scalar powers α = (α, . . . , α) and symmetric cones Ω. We give a more transparent proof, provide new examples, and briefly discuss a long standing open question regarding characterization of L boundedness for the case of vector indices α.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":"33 6","pages":"815-838"},"PeriodicalIF":0.6000,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Hilbert-type inequalities in homogeneous cones\",\"authors\":\"G. Garrigós, C. Nana\",\"doi\":\"10.4171/RLM/916\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove L-L bounds for the class of Hilbert-type operators associated with generalized powers Q in a homogeneous cone Ω. Our results extend and slightly improve earlier work from [10], where the problem was considered for scalar powers α = (α, . . . , α) and symmetric cones Ω. We give a more transparent proof, provide new examples, and briefly discuss a long standing open question regarding characterization of L boundedness for the case of vector indices α.\",\"PeriodicalId\":54497,\"journal\":{\"name\":\"Rendiconti Lincei-Matematica e Applicazioni\",\"volume\":\"33 6\",\"pages\":\"815-838\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti Lincei-Matematica e Applicazioni\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/RLM/916\",\"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":"Rendiconti Lincei-Matematica e Applicazioni","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/RLM/916","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove L-L bounds for the class of Hilbert-type operators associated with generalized powers Q in a homogeneous cone Ω. Our results extend and slightly improve earlier work from [10], where the problem was considered for scalar powers α = (α, . . . , α) and symmetric cones Ω. We give a more transparent proof, provide new examples, and briefly discuss a long standing open question regarding characterization of L boundedness for the case of vector indices α.
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