学术报告

题      目：Singular Integrals and Geometry

报  告  人：韩永生  教授  (邀请人：韩彦昌 )

                                   Auburn University

时      间：5月17日  15：30-16：30

地     点：数科院东楼401报告厅

报告人简介:

        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》。

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.

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