勷勤数学•专家报告

题      目：A real-variable method for multi-parameter  Harmonic Analysis associated with Zygmund dilations

报  告  人：  韩永生 教授  (邀请人：韩彦昌)

                                         美国奥本大学

时      间： 5月17日  09：00-10:00

地     点：数科院东楼507

报告人简介:

       韩永生教授是国际上知名的调和分析专家。美国奥本大学终身教授。本科毕业于北京大学，博士毕业于华盛顿大学师从于著名的数学家G.Weiss。 近四十年来致力于调和分析和函空间的理论研究。近年来已在国际主流的学术刊物上（Memoirs of ams, JFA, Math.Z,Transaction of ams等）发表论文100余篇。多次应邀在国际国内的重要的数学大会上作报告。

摘      要：

         In the famous paper ``On the existence of singular integrals'' appeared in Acta Mathematica in 1952, Calder\'on and Zygmunddeveloped a real-variable method for one-parameter harmonic analysis, which has had such widespread and influence in analysis.

In this talk, we will describe a real-variable method for multi-parameter harmonic analysis associated with Zygmund dilations. This method includes：

1. Singular integrals associated with Zygmund dilations, particularly, its regularity and cancellation conditions;

2. The continuous and discrete wavelet-type decompositions for $L^2$ functions;

3.The Littlewood-Paley theory associated with Zygmund dilations;

4. The Hardy and the Lipschitz function spaces and the boundedness of the above singular integrals on these spaces.