{"title":"一类奇异的双线性最大函数","authors":"Michael Christ, Zirui Zhou","doi":"10.1016/j.jfa.2024.110572","DOIUrl":null,"url":null,"abstract":"<div><p>Lebesgue space bounds <span><math><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo><mo>→</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></math></span> are established for certain singular maximal bilinear operators. The proof combines a single scale trilinear smoothing inequality with Calderón-Zygmund theory.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"287 8","pages":"Article 110572"},"PeriodicalIF":1.6000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002212362400260X/pdfft?md5=0872fa99d1fbac6f4059b1a6452ae02c&pid=1-s2.0-S002212362400260X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"A class of singular bilinear maximal functions\",\"authors\":\"Michael Christ, Zirui Zhou\",\"doi\":\"10.1016/j.jfa.2024.110572\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Lebesgue space bounds <span><math><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo><mo>→</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></math></span> are established for certain singular maximal bilinear operators. The proof combines a single scale trilinear smoothing inequality with Calderón-Zygmund theory.</p></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"287 8\",\"pages\":\"Article 110572\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-10-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S002212362400260X/pdfft?md5=0872fa99d1fbac6f4059b1a6452ae02c&pid=1-s2.0-S002212362400260X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002212362400260X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/7/4 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002212362400260X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/7/4 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Lebesgue space bounds are established for certain singular maximal bilinear operators. The proof combines a single scale trilinear smoothing inequality with Calderón-Zygmund theory.
期刊介绍：
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis
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