{"title":"p-adic Lebesgue 空间上尖锐最大函数换元的一些估计值","authors":"Jianglong Wu, Yunpeng Chang","doi":"10.1515/math-2023-0168","DOIUrl":null,"url":null,"abstract":"In this article, the main aim is to consider the boundedness of the nonlinear commutator of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic sharp maximal operator <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msubsup> <m:mrow> <m:mi mathvariant=\"script\">ℳ</m:mi> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mi>♯</m:mi> </m:mrow> </m:msubsup> </m:math> <jats:tex-math>{{\\mathcal{ {\\mathcal M} }}}_{p}^{\\sharp }</jats:tex-math> </jats:alternatives> </jats:inline-formula> with symbols belonging to the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_003.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic Lipschitz spaces in the context of the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic version of (variable) Lebesgue spaces, by which some new characterizations of the Lipschitz spaces are obtained in the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_005.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic field context.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some estimates for commutators of sharp maximal function on the p-adic Lebesgue spaces\",\"authors\":\"Jianglong Wu, Yunpeng Chang\",\"doi\":\"10.1515/math-2023-0168\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, the main aim is to consider the boundedness of the nonlinear commutator of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" 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xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic Lipschitz spaces in the context of the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_math-2023-0168_eq_004.png\\\" /> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic version of (variable) Lebesgue spaces, by which some new characterizations of the Lipschitz spaces are obtained in the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_math-2023-0168_eq_005.png\\\" /> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic field 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引用次数: 0
摘要
本文的主要目的是考虑 p p -adic 尖锐最大算子 ℳ p ♯ {\{mathcal{ {\mathcal M}}}_{p}^{\sharp } 的非线性换向器的有界性。}}}_{p}^{\sharp },符号属于 p p -adic Lipschitz 空间的(可变)Lebesgue 空间的 p p -adic 版本,通过这些符号,可以得到 p p -adic 场背景下 Lipschitz 空间的一些新特征。
Some estimates for commutators of sharp maximal function on the p-adic Lebesgue spaces
In this article, the main aim is to consider the boundedness of the nonlinear commutator of pp-adic sharp maximal operator ℳp♯{{\mathcal{ {\mathcal M} }}}_{p}^{\sharp } with symbols belonging to the pp-adic Lipschitz spaces in the context of the pp-adic version of (variable) Lebesgue spaces, by which some new characterizations of the Lipschitz spaces are obtained in the pp-adic field context.
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