Singular Integrals on Non-Smooth Domains in Real and Complex Analysis

实数和复数分析中非光滑域上的奇异积分

• 批准号: 0700815
• 负责人: William Feldman
• 金额: $ 13.15万
• 依托单位: University of Arkansas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0700815&HistoricalAwards=false
• 关键词: Singular; Integrals; Non; Smooth; Domains

Loredana Lanzani will study a number of problems in the areas of complex analyis and partial differential equations, with emphasis on the ambient domain's lack of boundary regularity. The probems to be studied include: integral representations of holomorphic functions on non-smooth domains; boundary regularity of Cauchy-type integrals; representations of Hardy spaces of boundary values of holomorphic functions. In order to study these classical problems of complex analysis in the non-classical context brought by the lack of smoothness, Loredana Lanzani and her collaborators will develop new techniques that hinge upon an interplay of real harmonic analysis and complex variables methods.

Loredana Lanzani将研究复分析和偏微分方程领域的一些问题，重点是环境域缺乏边界规则性。所要研究的问题包括：非光滑区域上全纯函数的积分表示，Cauchy型积分的边界正则性，全纯函数边值的哈代空间的表示。为了在非经典背景下研究这些经典的复分析问题，Loredana Lanzani和她的合作者将开发新的技术，这些技术取决于真实的调和分析和复变量方法的相互作用。