{"title":"有界对称域上Bergman空间上的Schatten类小Hankel算子","authors":"Wenwan Yang, Cheng Yuan","doi":"10.1016/j.jfa.2025.110875","DOIUrl":null,"url":null,"abstract":"<div><div>Suppose <span><math><mi>α</mi><mo>></mo><mo>−</mo><mn>1</mn></math></span>, <span><math><mfrac><mrow><mi>a</mi><mo>(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>N</mi><mo>+</mo><mi>α</mi></mrow></mfrac><mo><</mo><mi>p</mi><mo><</mo><mn>1</mn></math></span> and <em>f</em> belongs to the Bergman space <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> in the bounded symmetric domain Ω of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We prove that the little Hankel operator <span><math><msubsup><mrow><mi>h</mi></mrow><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>α</mi></mrow></msubsup></math></span> acting on <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> is in the Schatten <em>p</em>-class if and only if <em>f</em> is in the Besov space <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110875"},"PeriodicalIF":1.7000,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Schatten class little Hankel operators on Bergman spaces in bounded symmetric domains\",\"authors\":\"Wenwan Yang, Cheng Yuan\",\"doi\":\"10.1016/j.jfa.2025.110875\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Suppose <span><math><mi>α</mi><mo>></mo><mo>−</mo><mn>1</mn></math></span>, <span><math><mfrac><mrow><mi>a</mi><mo>(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>N</mi><mo>+</mo><mi>α</mi></mrow></mfrac><mo><</mo><mi>p</mi><mo><</mo><mn>1</mn></math></span> and <em>f</em> belongs to the Bergman space <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> in the bounded symmetric domain Ω of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We prove that the little Hankel operator <span><math><msubsup><mrow><mi>h</mi></mrow><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>α</mi></mrow></msubsup></math></span> acting on <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> is in the Schatten <em>p</em>-class if and only if <em>f</em> is in the Besov space <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>.</div></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"288 10\",\"pages\":\"Article 110875\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-02-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022123625000576\",\"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 Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123625000576","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Schatten class little Hankel operators on Bergman spaces in bounded symmetric domains
Suppose , and f belongs to the Bergman space in the bounded symmetric domain Ω of . We prove that the little Hankel operator acting on is in the Schatten p-class if and only if f is in the Besov space .
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