报告题目1：Boundedness of one-parameter Calder´on-Zygmund convolution operators on multi-parameter Hardy spaces

报告人：韩永生教授，Auburn University

报告时间：2025年3月24日（周一）14:30-15:30

报告地点：20-200

报告摘要：It is well known that the classical one-parameter Calder´on-Zygmund convolution operators are bounded on the classical one-parameter Hardy spaces. A natural question aries if the classical one-parameter Calder´on-Zygmund convolution operators are also bounded on the muliti-parameter Hardy spaces? In this talk, we describe positive answers to these questions. More precisely, we will consider all functions defined on R3 and three kinds of dilations given by 

δ_h:(x₁,x₂,x₃)→(δx₁,δx₂,δx₃),δ>0;

δ_h:(x₁,x₂,x₃)→(δ₁x₁,δ₂x₂,δ₃x₃),δ>0; 

and

δ_p:(₁,x₂,x₃)→(δ₁x₁,δ₂x₂,δ₃x₃),δ>0; 

and the singular integral convolution operators associated with these dilations.

报告题目2：Sinigular integrals in Dunkl setting

报告人：韩永生教授，Auburn University

报告时间：2025年3月25日（周二）14:30-15:30

报告地点：20-200

报告摘要：Consider the Euclidean space RN equipped with the reflection σα with respect to the hyperplane α⊥ orthogonal to a nonzero vector α given by σ_α(x)=x-2(〈x,α〉/ ‖α‖²)α. Then there are two metrics: for x,yx,y∈R^N, the Euclidean metric ‖x-y‖ and the Dunkl metric d(x,y)≔min_(σ∈G) ‖x-σ(y)‖, where G be the finite reflection group generated by the reflections σ_α. Let (R^N, ‖x-y‖, dω) and (R^N, d(x,y), dω) with the Dunkl measure dω be two spaces of homogeneous type in the sense of Coifman and Weiss, respectively. Then we should have two kinds of singular integrals. Motivited by the Dunkl-Riesz transforms, we have introduced a class of singular integrals which conver all singular integra convolution operators and the Ho ̈rmander multipliers in the Dunkl setting. Recentely, we develop the Dunkl-Calder´on commmutators which lead singular inetgral non-convolution operators in the Dunkl setting.

In this talk, we will describe the relationship between these four singular integrals and basic ideas for the proofs of the T1 theorems.

报告题目3：多参数算子的端点估计

报告人：韩永生教授，Auburn University

报告时间：2025年3月26日（周三）14:30-15:30

报告地点：20-306

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。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》。

邀请人：陈杰诚