{"title":"带加倍权重的加权伯格曼空间上黎曼-斯蒂尔特杰斯算子的基本规范","authors":"Lian Hu, Songxiao Li, Rong Yang","doi":"10.1515/gmj-2023-2110","DOIUrl":null,"url":null,"abstract":"Let ω be a doubling weight and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>0</m:mn> <m:mo><</m:mo> <m:mi>p</m:mi> <m:mo>≤</m:mo> <m:mi>q</m:mi> <m:mo><</m:mo> <m:mi mathvariant=\"normal\">∞</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2110_eq_0161.png\" /> <jats:tex-math>{0<p\\leq q<\\infty}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The essential norm of Riemann–Stieltjes operator <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>T</m:mi> <m:mi>g</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2110_eq_0210.png\" /> <jats:tex-math>{T_{g}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> from the weighted Bergman space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msubsup> <m:mi>A</m:mi> <m:mi>ω</m:mi> <m:mi>p</m:mi> </m:msubsup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2110_eq_0172.png\" /> <jats:tex-math>{A^{p}_{\\omega}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> to <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msubsup> <m:mi>A</m:mi> <m:mi>ω</m:mi> <m:mi>q</m:mi> </m:msubsup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2110_eq_0173.png\" /> <jats:tex-math>{A^{q}_{\\omega}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> was investigated in the unit ball of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>ℂ</m:mi> <m:mi>n</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2110_eq_0250.png\" /> <jats:tex-math>{\\mathbb{C}^{n}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Essential norm of Riemann–Stieltjes operator on weighted Bergman spaces with doubling weights\",\"authors\":\"Lian Hu, Songxiao Li, Rong Yang\",\"doi\":\"10.1515/gmj-2023-2110\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let ω be a doubling weight and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mn>0</m:mn> <m:mo><</m:mo> <m:mi>p</m:mi> <m:mo>≤</m:mo> <m:mi>q</m:mi> <m:mo><</m:mo> <m:mi mathvariant=\\\"normal\\\">∞</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2110_eq_0161.png\\\" /> <jats:tex-math>{0<p\\\\leq q<\\\\infty}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The essential norm of Riemann–Stieltjes operator <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msub> <m:mi>T</m:mi> <m:mi>g</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2110_eq_0210.png\\\" /> <jats:tex-math>{T_{g}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> from the weighted Bergman space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msubsup> <m:mi>A</m:mi> <m:mi>ω</m:mi> <m:mi>p</m:mi> </m:msubsup> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2110_eq_0172.png\\\" /> <jats:tex-math>{A^{p}_{\\\\omega}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> to <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msubsup> <m:mi>A</m:mi> <m:mi>ω</m:mi> <m:mi>q</m:mi> </m:msubsup> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2110_eq_0173.png\\\" /> <jats:tex-math>{A^{q}_{\\\\omega}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> was investigated in the unit ball of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msup> <m:mi>ℂ</m:mi> <m:mi>n</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2110_eq_0250.png\\\" /> <jats:tex-math>{\\\\mathbb{C}^{n}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2023-2110\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2023-2110","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设 ω 为加倍权重,且 0 < p ≤ q < ∞ {0<p\leq q<\infty} 。在 ℂ n {mathbb{C}^{n} 的单位球中研究了从加权伯格曼空间 A ω p {A^{p}_{\omega}} 到 A ω q {A^{q}_{\omega}} 的黎曼-斯蒂尔杰斯算子 T g {T_{g}} 的基本规范。} .
Essential norm of Riemann–Stieltjes operator on weighted Bergman spaces with doubling weights
Let ω be a doubling weight and 0<p≤q<∞{0<p\leq q<\infty}. The essential norm of Riemann–Stieltjes operator Tg{T_{g}} from the weighted Bergman space Aωp{A^{p}_{\omega}} to Aωq{A^{q}_{\omega}} was investigated in the unit ball of ℂn{\mathbb{C}^{n}}.