Singular Integrals and Geometry
数学专题报告
报告题目(Title)：Singular Integrals and Geometry
报告人(Speaker)：韩永生（美国Auburn大学）
地点(Place)：后主楼1124
时间(Time)：6月13日(周四)，15:00-16:00
邀请人(Inviter)：杨大春
报告摘要
It was well known that geometric considerations enter in a decisive way in many questions of analysis. As Meyer, the recipient of the 2017 Abel Prize, remarked “One is amazed by the dramatic changes that occurred in analysis during the twentieth century. In the 1930s complex methods and Fourier series played a seminal role. After many improvements, mostly achieved by the Calder´on–Zygmund school, the action takes place today on spaces of homogeneous type. No group structure is available, the Fourier transform is missing, but a version of harmonic analysis is still present. Indeed the geometry is conducting the analysis.”
In this talk, we will concentrate on questions that how the geometrical considerations play a crucial role in the theory of singular integrals. We will attempt to give a broad overview of the descriptions of the singular integrals, such as, nonstandard singular integrals which include the flag singular integrals, singular integrals in the Dunkl setting and the singular integrals associated with the Zygmund dilations.
主讲人简介
韩永生教授1981 年于北京大学获得硕士学位，1984 年在美国Washington University 大学师从鼎鼎大名的调和分析大师G. Weiss 教授，获得博士学位。目前，他是美国Auburn 大学数学系终身教授。韩永生教授长期从事调和分析的教学与研究，尤其是函数空间理论，已在国内外期刊Trans. Amer. Math. Soc., Forum Math., Ann. Scuola Norm. Sup. Pisa Cl. Sci., J. Geometric Analysis, Journal of Functional Analysis, Revista Mathematica Iberoamericana, Analysis and PDE, Mem. Amer. Math. Soc., Math. Z.等杂志发表学术论文100 余篇。撰写出版专著《Harmonic Analysis on Spaces of Homogeneous Type》，《Hp 空间》，《近代调和分析方法及其应用》。
