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

点击翻译按钮获取中文摘要

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.