报告题目：GEOMETRY AND HARDY SPACES

报告人：韩永生 教授

时 间：2018年4月23日(周一) 上午10:30-11:30

地 点：工商管理楼200-9

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 a question that how the geometrical considerations play a crucial role in the theory of the Hardy space. We shall begin by recalling the theory of the Hardy space on the Euclidean space. To be precise, we will attempt to give a broad overview of the characterizations of the Hardy space via the Littlewood{Paley theory and atomic decomposition. we then take up these same topics in more general settings such as domains in Rn or space of homogeneous type (X; d; _) in the sense of Coifman and Weiss, and discuss the geometrical considerations on the quasi-metric d and the measure.

报告人简介：

韩永生教授是国际知名的调和分析专家。1978年于北京大学师从我国著名的数学家程民德院士和邓东皋教授学习调和分析，于1981年4月获硕士学位。1981年8月赴美国华盛顿大学师从世界调和分析大师G. Weiss教授，并于1984年获得博士学位。

目前，韩教授是美国奥本大学数学系终身教授，并长期从事调和分析的教学与研究，尤其是函数空间理论，已在国内外学术期刊Mem. Amer. Math. Soc., Trans. Amer. Math. Soc., J. Geom. Anal., J. Funct. Anal., Proc. Am. Math. Soc., Diss. Math., Ann. Sc. Norm. Cl. Sci., Rev. Mat. Iberoam., Stud. Math., Math. Z., Math. Res. Lett., J. Fourier Anal. Appl.,Sci. China Math.等杂志上发表近百篇高水平学术论文。撰写出版专著《Harmonic Analysis on Spaces of Homogeneous Type》，《H^p空间》，《近代调和分析方法及其应用》等。韩教授是国际上调和分析研究领域享有良好声誉的数学家，现担任多家国际数学杂志编委，并多次在国际数学会议上受邀作报告。

联系人：王梦（mathdreamcn@zju.edu.cn）

欢迎广大师生参加！