{"title":"Bergmann空间上的广义Hausdorff算子","authors":"Sasikala Perumal, Kalaivani Kamalakkannan","doi":"10.1515/conop-2023-0101","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we considered the generalized Hausdorff operator <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">ℋ</m:mi> </m:mrow> <m:mrow> <m:mi>μ</m:mi> <m:mo>,</m:mo> <m:mi>ϕ</m:mi> <m:mo>,</m:mo> <m:mi>a</m:mi> </m:mrow> </m:msub> </m:math> {{\\mathcal{ {\\mathcal H} }}}_{\\mu ,\\phi ,a} on Bergmann space and determined the conditions on <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>ϕ</m:mi> </m:math> \\phi and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>a</m:mi> </m:math> a so that the operator is bounded. In addition, we studied the action of the Hausdorff operator on the truncated domain to estimate norm <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">ℋ</m:mi> </m:mrow> <m:mrow> <m:mi>μ</m:mi> <m:mo>,</m:mo> <m:mi>ϕ</m:mi> <m:mo>,</m:mo> <m:mi>a</m:mi> </m:mrow> </m:msub> </m:math> {{\\mathcal{ {\\mathcal H} }}}_{\\mu ,\\phi ,a} and established a relation with quasi-Hausdorff operator on Bergmann space.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Hausdorff operator on Bergmann spaces\",\"authors\":\"Sasikala Perumal, Kalaivani Kamalakkannan\",\"doi\":\"10.1515/conop-2023-0101\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this article, we considered the generalized Hausdorff operator <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msub> <m:mrow> <m:mi class=\\\"MJX-tex-caligraphic\\\" mathvariant=\\\"script\\\">ℋ</m:mi> </m:mrow> <m:mrow> <m:mi>μ</m:mi> <m:mo>,</m:mo> <m:mi>ϕ</m:mi> <m:mo>,</m:mo> <m:mi>a</m:mi> </m:mrow> </m:msub> </m:math> {{\\\\mathcal{ {\\\\mathcal H} }}}_{\\\\mu ,\\\\phi ,a} on Bergmann space and determined the conditions on <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>ϕ</m:mi> </m:math> \\\\phi and <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>a</m:mi> </m:math> a so that the operator is bounded. In addition, we studied the action of the Hausdorff operator on the truncated domain to estimate norm <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msub> <m:mrow> <m:mi class=\\\"MJX-tex-caligraphic\\\" mathvariant=\\\"script\\\">ℋ</m:mi> </m:mrow> <m:mrow> <m:mi>μ</m:mi> <m:mo>,</m:mo> <m:mi>ϕ</m:mi> <m:mo>,</m:mo> <m:mi>a</m:mi> </m:mrow> </m:msub> </m:math> {{\\\\mathcal{ {\\\\mathcal H} }}}_{\\\\mu ,\\\\phi ,a} and established a relation with quasi-Hausdorff operator on Bergmann space.\",\"PeriodicalId\":53800,\"journal\":{\"name\":\"Concrete Operators\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Concrete Operators\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/conop-2023-0101\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2023-0101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Abstract In this article, we considered the generalized Hausdorff operator ℋμ,ϕ,a {{\mathcal{ {\mathcal H} }}}_{\mu ,\phi ,a} on Bergmann space and determined the conditions on ϕ \phi and a a so that the operator is bounded. In addition, we studied the action of the Hausdorff operator on the truncated domain to estimate norm ℋμ,ϕ,a {{\mathcal{ {\mathcal H} }}}_{\mu ,\phi ,a} and established a relation with quasi-Hausdorff operator on Bergmann space.
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