{"title":"福克空间上豪斯多夫算子的有界性和紧凑性","authors":"Óscar Blasco, Antonio Galbis","doi":"10.1090/tran/9133","DOIUrl":null,"url":null,"abstract":"<p>We obtain a complete characterization of the bounded Hausdorff operators acting on a Fock space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F Subscript alpha Superscript p\"> <mml:semantics> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mi>α</mml:mi> <mml:mi>p</mml:mi> </mml:msubsup> <mml:annotation encoding=\"application/x-tex\">F^p_\\alpha</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and taking its values into a larger one <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F Subscript alpha Superscript q Baseline comma 0 greater-than p less-than-or-equal-to q less-than-or-equal-to normal infinity\"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mi>α</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:mo>,</mml:mo> <mml:mtext> </mml:mtext> <mml:mn>0</mml:mn> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>q</mml:mi> <mml:mo>≤</mml:mo> <mml:mi mathvariant=\"normal\">∞</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">F^q_\\alpha ,\\ 0 > p \\leq q \\leq \\infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, as well as some necessary or sufficient conditions for a Hausdorff operator to transform a Fock space into a smaller one. Some results are written in the context of mixed norm Fock spaces. Also the compactness of Hausdorff operators on a Fock space is characterized. The compactness result for Hausdorff operators on the Fock space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F Subscript alpha Superscript normal infinity\"> <mml:semantics> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mi>α</mml:mi> <mml:mi mathvariant=\"normal\">∞</mml:mi> </mml:msubsup> <mml:annotation encoding=\"application/x-tex\">F^\\infty _\\alpha</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is extended to more general Banach spaces of entire functions with weighted sup norms defined in terms of a radial weight and conditions for the Hausdorff operators to become <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-summing are also included.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boundedness and compactness of Hausdorff operators on Fock spaces\",\"authors\":\"Óscar Blasco, Antonio Galbis\",\"doi\":\"10.1090/tran/9133\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We obtain a complete characterization of the bounded Hausdorff operators acting on a Fock space <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper F Subscript alpha Superscript p\\\"> <mml:semantics> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mi>α</mml:mi> <mml:mi>p</mml:mi> </mml:msubsup> <mml:annotation encoding=\\\"application/x-tex\\\">F^p_\\\\alpha</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and taking its values into a larger one <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper F Subscript alpha Superscript q Baseline comma 0 greater-than p less-than-or-equal-to q less-than-or-equal-to normal infinity\\\"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mi>α</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:mo>,</mml:mo> <mml:mtext> </mml:mtext> <mml:mn>0</mml:mn> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>q</mml:mi> <mml:mo>≤</mml:mo> <mml:mi mathvariant=\\\"normal\\\">∞</mml:mi> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">F^q_\\\\alpha ,\\\\ 0 > p \\\\leq q \\\\leq \\\\infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, as well as some necessary or sufficient conditions for a Hausdorff operator to transform a Fock space into a smaller one. Some results are written in the context of mixed norm Fock spaces. Also the compactness of Hausdorff operators on a Fock space is characterized. 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引用次数: 0
摘要
我们得到了作用于Fock空间F α p F^p_\alpha 并将其值转化为更大的F α q , 0 > p ≤ q ≤ ∞ F^q_\alpha ,\ 0 > p \leq q \leq \infty 的有界Hausdorff算子的完整描述，以及Hausdorff算子将Fock空间转化为更小的Fock空间的一些必要或充分条件。一些结果是在混合规范 Fock 空间的背景下写出的。此外，还描述了福克空间上豪斯多夫算子的紧凑性。福克空间 F α ∞ F^\infty _\alpha 上豪斯多夫算子的紧凑性结果被扩展到更一般的全函数巴纳赫空间，其加权超规范是以径向权重定义的，豪斯多夫算子成为 p p - 和的条件也包括在内。
Boundedness and compactness of Hausdorff operators on Fock spaces
We obtain a complete characterization of the bounded Hausdorff operators acting on a Fock space FαpF^p_\alpha and taking its values into a larger one Fαq,0>p≤q≤∞F^q_\alpha ,\ 0 > p \leq q \leq \infty, as well as some necessary or sufficient conditions for a Hausdorff operator to transform a Fock space into a smaller one. Some results are written in the context of mixed norm Fock spaces. Also the compactness of Hausdorff operators on a Fock space is characterized. The compactness result for Hausdorff operators on the Fock space Fα∞F^\infty _\alpha is extended to more general Banach spaces of entire functions with weighted sup norms defined in terms of a radial weight and conditions for the Hausdorff operators to become pp-summing are also included.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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