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

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。

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.