一、报告题目：T1 Theorem in Dunkl Setting

二、报告人：Professor Yongsheng Han

三、时 间：2024年5月24日(周五) 9:00—11:00

四、地 点：闻理园 A4—309

报告摘要：We establish the T1 theorem for a new class of (non-convolution type) singular integral op- erators in the Dunkl setting which is associated with finite reflection groups on the Euclidean space. This group structure induces two nonequivalent metrics: the Euclidean metric and the Dunkl metric, which are both involved in the estimates of singular integrals, heat and Poisson kernels in this Dunkl setting. As an application, we establish the Littlewood–Paley theory in the Dunkl setting, where the L2 boundedness plays a crucial role. New tools developed in this paper include the weak-type discrete Caldero ́n reproducing formulae, Coifman-type approximation to the identity, Meyer-type commutation Lemma, and new almost orthogonal estimates in the Dunkl setting. Joint work with Ming-Yi Lee, Ji Li and Chaoqian Tan.

报告人简介：韩永生教授是国际知名的调和分析专家。先后在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，在美国华盛顿大学师从世界调和分析大师G. Weiss教授。韩永生是美国奥本大学数学系终身教授，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.等高影响期刊上发表140余篇高水平学术论文。SCI他引1000多次，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。韩永生目前担任多家国际数学杂志编委。

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