勷勤数学•专家报告

题      目：A new approach to Hardy spaces associated with Zygmund dilations

报  告  人：韩永生 教授  (邀请人：韩彦昌)

                                             奥本大学

时      间：6月24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。

摘      要：

       In this talk, we will describe a new approach to Hardy spaces associated with Zygmund dilations. More precisely, we begin with an approximation to the identity associated with the Zygmund dilations and establish a new wavelet-type deconposition in L^2. Baced on this deconposition, the Littlewood-Paley square function is defined. Then we define the Hardy space norm for L^2 functions and prove that the wavelet-type deconposition holds for the Hardy spaces norm with the L^2

functions. By a duality argument between the Hay spaces and CMOp

spaces, the final Hardy space is defined by all distributions in L^2 ∩ CMOp

with wavelet-type deconposition. This final Hardy space is eqivalent to one introduced in [HLLTW].