P.非交换马氏哈代空间的琼斯插值定理 II

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-17 DOI:10.1112/jlms.12968

Narcisse Randrianantoanina

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For <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 <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 <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 <math>\n <semantics>\n <mi>p</mi>\n <annotation>$p$</annotation>\n </semantics></math>. We prove the following real interpolation identity: If <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 <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 ","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"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\":\"Let <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 <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 <math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$\\\\mathcal {M}$</annotation>\\n </semantics></math>. 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We prove the following real interpolation identity: If <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 <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 \",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12968\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12968","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","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

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P. Jones' interpolation theorem for noncommutative martingale Hardy spaces II

Let $M$ be a semifinite von Neumann algebra equipped with an increasing filtration ${(M_{n})}_{n ⩾ 1}$ of (semifinite) von Neumann subalgebras of $M$ . For $1 ⩽ p ⩽ \infty$ , let $H_{p}^{c} (M)$ denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration ${(M_{n})}_{n ⩾ 1}$ and the index $p$ . We prove the following real interpolation identity: If $0 < θ < 1$ and $1 / p = 1 - θ$ , then

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.