{"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}
引用次数: 0
Abstract
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
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