Holomorphic Singular Integrals on Non-Smooth Domains in Complex Analysis

Loredana Lanzani和她的合作者将探索几个复杂变量和偏微分方程领域的一些基本问题，重点是环境域缺乏边界规则性。为了实现这些目标，Loredana Lanzani和她的合作者将开发新的技术，这些技术依赖于复杂分析和谐波分析的相互作用。几种复变、调和分析和偏微分方程是数学的主要分支。它们在纯科学和应用科学中具有至高无上的重要性，并对我们今天对传热和天体力学等基本现象的理解作出了巨大贡献。

Loredana Lanzani and her collaborators will explore a number of fundamental questions in the area of Several Complex Variables and Partial Differential Equations, with emphasis onthe ambient domain's lack of boundary regularity. To accomplish these goals Loredana Lanzani and her collaborators will develop new techniques that hinge upon an interplay of complex analysis and harmonic analysis.Several Complex Variables, Harmonic Analysis and Partial Differential Equations are major branches of mathematics. They are of paramount importance in pure and applied sciences and have vastly contributed to our present-day understanding of such basic phenomena as heat transfer and celestial mechanics.