有界对称域中的局部锥乘数和考奇-塞格投影

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-12 DOI:10.1112/jlms.12986

Fernando Ballesta Yagüe, Gustavo Garrigós

{"title":"有界对称域中的局部锥乘数和考奇-塞格投影","authors":"Fernando Ballesta Yagüe, Gustavo Garrigós","doi":"10.1112/jlms.12986","DOIUrl":null,"url":null,"abstract":"We show that the cone multiplier satisfies local <math>\n <semantics>\n <msup>\n <mi>L</mi>\n <mi>p</mi>\n </msup>\n <annotation>$L^p$</annotation>\n </semantics></math>-<math>\n <semantics>\n <msup>\n <mi>L</mi>\n <mi>q</mi>\n </msup>\n <annotation>$L^q$</annotation>\n </semantics></math> bounds only in the trivial range <math>\n <semantics>\n <mrow>\n <mn>1</mn>\n <mo>⩽</mo>\n <mi>q</mi>\n <mo>⩽</mo>\n <mn>2</mn>\n <mo>⩽</mo>\n <mi>p</mi>\n <mo>⩽</mo>\n <mi>∞</mi>\n </mrow>\n <annotation>$1\\leqslant q\\leqslant 2\\leqslant p\\leqslant \\infty$</annotation>\n </semantics></math>. To do so, we suitably adapt to this setting the proof of Fefferman for the ball multiplier. As a consequence we answer negatively a question by Békollé and Bonami, regarding the continuity from <math>\n <semantics>\n <mrow>\n <msup>\n <mi>L</mi>\n <mi>p</mi>\n </msup>\n <mo>→</mo>\n <msup>\n <mi>L</mi>\n <mi>q</mi>\n </msup>\n </mrow>\n <annotation>$L^p\\rightarrow L^q$</annotation>\n </semantics></math> of the Cauchy–Szegö projections associated with a class of bounded symmetric domains in <math>\n <semantics>\n <msup>\n <mi>C</mi>\n <mi>n</mi>\n </msup>\n <annotation>${\\mathbb {C}}^n$</annotation>\n </semantics></math> with rank <math>\n <semantics>\n <mrow>\n <mi>r</mi>\n <mo>⩾</mo>\n <mn>2</mn>\n </mrow>\n <annotation>$r\\geqslant 2$</annotation>\n </semantics></math>.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12986","citationCount":"0","resultStr":"{\"title\":\"Local cone multipliers and Cauchy–Szegö projections in bounded symmetric domains\",\"authors\":\"Fernando Ballesta Yagüe, Gustavo Garrigós\",\"doi\":\"10.1112/jlms.12986\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the cone multiplier satisfies local <math>\\n <semantics>\\n <msup>\\n <mi>L</mi>\\n <mi>p</mi>\\n </msup>\\n <annotation>$L^p$</annotation>\\n </semantics></math>-<math>\\n <semantics>\\n <msup>\\n <mi>L</mi>\\n <mi>q</mi>\\n </msup>\\n <annotation>$L^q$</annotation>\\n </semantics></math> bounds only in the trivial range <math>\\n <semantics>\\n <mrow>\\n <mn>1</mn>\\n <mo>⩽</mo>\\n <mi>q</mi>\\n <mo>⩽</mo>\\n <mn>2</mn>\\n <mo>⩽</mo>\\n <mi>p</mi>\\n <mo>⩽</mo>\\n <mi>∞</mi>\\n </mrow>\\n <annotation>$1\\\\leqslant q\\\\leqslant 2\\\\leqslant p\\\\leqslant \\\\infty$</annotation>\\n </semantics></math>. To do so, we suitably adapt to this setting the proof of Fefferman for the ball multiplier. As a consequence we answer negatively a question by Békollé and Bonami, regarding the continuity from <math>\\n <semantics>\\n <mrow>\\n <msup>\\n <mi>L</mi>\\n <mi>p</mi>\\n </msup>\\n <mo>→</mo>\\n <msup>\\n <mi>L</mi>\\n <mi>q</mi>\\n </msup>\\n </mrow>\\n <annotation>$L^p\\\\rightarrow L^q$</annotation>\\n </semantics></math> of the Cauchy–Szegö projections associated with a class of bounded symmetric domains in <math>\\n <semantics>\\n <msup>\\n <mi>C</mi>\\n <mi>n</mi>\\n </msup>\\n <annotation>${\\\\mathbb {C}}^n$</annotation>\\n </semantics></math> with rank <math>\\n <semantics>\\n <mrow>\\n <mi>r</mi>\\n <mo>⩾</mo>\\n <mn>2</mn>\\n </mrow>\\n <annotation>$r\\\\geqslant 2$</annotation>\\n </semantics></math>.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12986\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12986\",\"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.12986","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

我们证明，锥乘法器仅在微不足道的范围 1 ⩽ q ⩽ 2 ⩽ p ⩽ ∞ 1\leqslant q\leqslant 2\leqslant p\leqslant \infty$ 中满足局部 L p $L^p$ - L q $L^q$ 约束。为此，我们把费弗曼对球乘法器的证明适当地调整到这个环境中。因此，我们否定地回答了贝科雷和博纳米提出的一个问题，即从 L p → L q $L^p\rightarrow L^q$ 与 C n 中一类秩为 r ⩾ 2 $r\geqslant 2$ 的有界对称域相关的考奇-塞戈投影的连续性问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Local cone multipliers and Cauchy–Szegö projections in bounded symmetric domains

查看原文本刊更多论文

Local cone multipliers and Cauchy–Szegö projections in bounded symmetric domains

We show that the cone multiplier satisfies local $L^{p}$ - $L^{q}$ bounds only in the trivial range $1 ⩽ q ⩽ 2 ⩽ p ⩽ \infty$ . To do so, we suitably adapt to this setting the proof of Fefferman for the ball multiplier. As a consequence we answer negatively a question by Békollé and Bonami, regarding the continuity from $L^{p} \to L^{q}$ of the Cauchy–Szegö projections associated with a class of bounded symmetric domains in $C^{n}$ with rank $r ⩾ 2$ .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.