学术报告

题      目： SINGULAR INTEGRAL, WEVELET-TYPE DECOMPOSION, LITTLEWOOD-PALEY AND HARDY SPACE IN DUNKL SETTING

报  告  人：韩永生   教授  (邀请人：韩彦昌 )

          Department of Mathematics, Auburn University, Auburn, AL 36849, U.S.A

时      间：4月3日  11：00-12：00

地     点：数科院阶梯二楼报告厅

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。

摘      要：

       In this talk, we first introduce a new class of singular integral operators in the Dunkl setting which is associated with finite reflection groups on the Euclidean space. The group structures induce two nonequivalent metrics: the Euclidean metric and the Dunkl metric, which both
are involved in the estimates of singular integrals, the heat and Poisson kernels. Applying this new singular integrals, namely the T1 theorem, the criterion of the L 2 boundedness in Dunkl setting, the wevelet-type decomposion is established and the Littlewood-Paley theory is developed. Finally, the Hardy space theory in the Dunkl setting is provided.