{"title":"P.非交换马氏哈代空间的琼斯插值定理 II","authors":"Narcisse Randrianantoanina","doi":"10.1112/jlms.12968","DOIUrl":null,"url":null,"abstract":"<p>Let <span></span><math>\n <semantics>\n <mi>M</mi>\n <annotation>$\\mathcal {M}$</annotation>\n </semantics></math> be a semifinite von Neumann algebra equipped with an increasing filtration <span></span><math>\n <semantics>\n <msub>\n <mrow>\n <mo>(</mo>\n <msub>\n <mi>M</mi>\n <mi>n</mi>\n </msub>\n <mo>)</mo>\n </mrow>\n <mrow>\n <mi>n</mi>\n <mo>⩾</mo>\n <mn>1</mn>\n </mrow>\n </msub>\n <annotation>$(\\mathcal {M}_n)_{n\\geqslant 1}$</annotation>\n </semantics></math> of (semifinite) von Neumann subalgebras of <span></span><math>\n <semantics>\n <mi>M</mi>\n <annotation>$\\mathcal {M}$</annotation>\n </semantics></math>. For <span></span><math>\n <semantics>\n <mrow>\n <mn>1</mn>\n <mo>⩽</mo>\n <mi>p</mi>\n <mo>⩽</mo>\n <mi>∞</mi>\n </mrow>\n <annotation>$1\\leqslant p \\leqslant \\infty$</annotation>\n </semantics></math>, let <span></span><math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>H</mi>\n <mi>p</mi>\n <mi>c</mi>\n </msubsup>\n <mrow>\n <mo>(</mo>\n <mi>M</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\mathcal {H}_p^c(\\mathcal {M})$</annotation>\n </semantics></math> denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration <span></span><math>\n <semantics>\n <msub>\n <mrow>\n <mo>(</mo>\n <msub>\n <mi>M</mi>\n <mi>n</mi>\n </msub>\n <mo>)</mo>\n </mrow>\n <mrow>\n <mi>n</mi>\n <mo>⩾</mo>\n <mn>1</mn>\n </mrow>\n </msub>\n <annotation>$(\\mathcal {M}_n)_{n\\geqslant 1}$</annotation>\n </semantics></math> and the index <span></span><math>\n <semantics>\n <mi>p</mi>\n <annotation>$p$</annotation>\n </semantics></math>. We prove the following real interpolation identity: If <span></span><math>\n <semantics>\n <mrow>\n <mn>0</mn>\n <mo><</mo>\n <mi>θ</mi>\n <mo><</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$0&lt;\\theta &lt;1$</annotation>\n </semantics></math> and <span></span><math>\n <semantics>\n <mrow>\n <mn>1</mn>\n <mo>/</mo>\n <mi>p</mi>\n <mo>=</mo>\n <mn>1</mn>\n <mo>−</mo>\n <mi>θ</mi>\n </mrow>\n <annotation>$1/p=1-\\theta$</annotation>\n </semantics></math>, then\n\n </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"P. Jones' interpolation theorem for noncommutative martingale Hardy spaces II\",\"authors\":\"Narcisse Randrianantoanina\",\"doi\":\"10.1112/jlms.12968\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <span></span><math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$\\\\mathcal {M}$</annotation>\\n </semantics></math> be a semifinite von Neumann algebra equipped with an increasing filtration <span></span><math>\\n <semantics>\\n <msub>\\n <mrow>\\n <mo>(</mo>\\n <msub>\\n <mi>M</mi>\\n <mi>n</mi>\\n </msub>\\n <mo>)</mo>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n <mo>⩾</mo>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <annotation>$(\\\\mathcal {M}_n)_{n\\\\geqslant 1}$</annotation>\\n </semantics></math> of (semifinite) von Neumann subalgebras of <span></span><math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$\\\\mathcal {M}$</annotation>\\n </semantics></math>. For <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>1</mn>\\n <mo>⩽</mo>\\n <mi>p</mi>\\n <mo>⩽</mo>\\n <mi>∞</mi>\\n </mrow>\\n <annotation>$1\\\\leqslant p \\\\leqslant \\\\infty$</annotation>\\n </semantics></math>, let <span></span><math>\\n <semantics>\\n <mrow>\\n <msubsup>\\n <mi>H</mi>\\n <mi>p</mi>\\n <mi>c</mi>\\n </msubsup>\\n <mrow>\\n <mo>(</mo>\\n <mi>M</mi>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$\\\\mathcal {H}_p^c(\\\\mathcal {M})$</annotation>\\n </semantics></math> denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration <span></span><math>\\n <semantics>\\n <msub>\\n <mrow>\\n <mo>(</mo>\\n <msub>\\n <mi>M</mi>\\n <mi>n</mi>\\n </msub>\\n <mo>)</mo>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n <mo>⩾</mo>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <annotation>$(\\\\mathcal {M}_n)_{n\\\\geqslant 1}$</annotation>\\n </semantics></math> and the index <span></span><math>\\n <semantics>\\n <mi>p</mi>\\n <annotation>$p$</annotation>\\n </semantics></math>. We prove the following real interpolation identity: If <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>0</mn>\\n <mo><</mo>\\n <mi>θ</mi>\\n <mo><</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$0&lt;\\\\theta &lt;1$</annotation>\\n </semantics></math> and <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>1</mn>\\n <mo>/</mo>\\n <mi>p</mi>\\n <mo>=</mo>\\n <mn>1</mn>\\n <mo>−</mo>\\n <mi>θ</mi>\\n </mrow>\\n <annotation>$1/p=1-\\\\theta$</annotation>\\n </semantics></math>, then\\n\\n </p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12968\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12968","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
让 M $\mathcal {M}$ 是一个半有穷 von Neumann 代数，其上有 M $\mathcal {M}$ 的（半有穷）von Neumann 子代数的递增滤波 ( M n ) n ⩾ 1 $(\mathcal {M}_n)_{n\geqslant 1}$ 。对于 1 ⩽ p ⩽ ∞ $1\leqslant p \leqslant \infty$ 、让 H p c ( M ) $\mathcal {H}_p^c(\mathcal {M})$ 表示由与滤波 ( M n ) n ⩾ 1 $(\mathcal {M}_n)_{n\geqslant 1}$ 和索引 p $p$ 相关的列平方函数构造的非交换列鞅哈代空间。我们证明下面的实插值特性：如果 0 < θ < 1 $0<\theta <1$ 和 1 / p = 1 - θ $1/p=1-\theta$ , 那么
P. Jones' interpolation theorem for noncommutative martingale Hardy spaces II
Let be a semifinite von Neumann algebra equipped with an increasing filtration of (semifinite) von Neumann subalgebras of . For , let denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration and the index . We prove the following real interpolation identity: If and , then
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