一、报告题目：Littlewood-Paley Theory and Hardy Spaces in Multiparameter Analysis

二、报告人：韩永生 教授

三、时 间：2018年4月23日(周一)下午15:00---16:00

四、地 点：闻理园A4-305室 

五、报告摘要：

Multiparameter analysis began with Zygmund strong maximal function and Marcinkiewicz multiplier, and continued with Stein, Gundy, Fefferman, Chang and Journel's works on singular integrals, Hardy and BMO spaces on the product Euclidean space. Multiparameter analysis appeared first implicitly in the work of Phong and Stein when they studied some classes of pseudo-differential and singular integral operators that arise typically in non-coercive boundary-value problems for elliptic equations. The Marcinkiewicz multiplier on the Heisenberg groups was an excellent example of multiparameter singular integrals. Muller-Ricci-Stein proved its boundedness on L^p and introduced flag singular integrals. Very recently, Stein-Yung study the phenomena that arise when one combines the classical pseudo-differential operators with those operators appeared in the subelliptic estimates, and on strongly pseudoconvex domains, They introduced a new pseudo-differential operators which contain the standard "isotropic" and "ono-isotropic" pseudo-differential operators. They obtained the L^p boundedness and showed that this new class forms an algebra.

In this talk, we will describe the Littlewood-Paley theory and the Hardy spaces in multi-parameter analysis. Particularly, we will concentrate on Stein-Yung's work.^

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。

      欢迎广大师生参加！   

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                                                                                                           应用数学研究所  

                                                                                     2018年4月12日