{"title":"对偶Hardy空间中的柯西变换和塞格格投影:不等式和Möbius不变性","authors":"David E. Barrett , Luke D. Edholm","doi":"10.1016/j.jfa.2025.110980","DOIUrl":null,"url":null,"abstract":"<div><div>Dual pairs of interior and exterior Hardy spaces associated to a simple closed Lipschitz planar curve are considered, leading to a Möbius invariant function bounding the norm of the Cauchy transform <strong><em>C</em></strong> from below. This function is shown to satisfy strong rigidity properties and is closely connected via the Berezin transform to the square of the Kerzman-Stein operator. Explicit example calculations are presented. For ellipses, a new asymptotically sharp lower bound on the norm of <strong><em>C</em></strong> is produced.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110980"},"PeriodicalIF":1.7000,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cauchy transforms and Szegő projections in dual Hardy spaces: Inequalities and Möbius invariance\",\"authors\":\"David E. Barrett , Luke D. Edholm\",\"doi\":\"10.1016/j.jfa.2025.110980\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Dual pairs of interior and exterior Hardy spaces associated to a simple closed Lipschitz planar curve are considered, leading to a Möbius invariant function bounding the norm of the Cauchy transform <strong><em>C</em></strong> from below. This function is shown to satisfy strong rigidity properties and is closely connected via the Berezin transform to the square of the Kerzman-Stein operator. Explicit example calculations are presented. For ellipses, a new asymptotically sharp lower bound on the norm of <strong><em>C</em></strong> is produced.</div></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"289 6\",\"pages\":\"Article 110980\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-03-31\",\"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/S0022123625001624\",\"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/S0022123625001624","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Cauchy transforms and Szegő projections in dual Hardy spaces: Inequalities and Möbius invariance
Dual pairs of interior and exterior Hardy spaces associated to a simple closed Lipschitz planar curve are considered, leading to a Möbius invariant function bounding the norm of the Cauchy transform C from below. This function is shown to satisfy strong rigidity properties and is closely connected via the Berezin transform to the square of the Kerzman-Stein operator. Explicit example calculations are presented. For ellipses, a new asymptotically sharp lower bound on the norm of C is produced.
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