勷勤数学•专家报告

题      目：Distributional estimates in probability theory and harmonic analysis

报  告  人： Dmitriy Zanin 教授  (邀请人：范智杰)

                                          中南大学

时      间： 3月19日  15：30-16:30

地     点：数科院东楼401

报告人简介:

       Dmitriy Zanin, 中南大学教授, 长期从事泛函分析、算子代数与非交换几何等方向的研究，在 Amer. J. Math., Proc. Lond. Math. Soc., J. Reine Angew. Math., Math. Ann., Adv. Math., Comm. Math. Phys. 和 J. Funct. Anal. 等国际知名期刊发表学术论文100余篇，并获得 ARC Discovery Project、UNSW Scientia Fellowship 及 Australian Research Council DECRA Fellowship 等项目资助。

摘      要：

       Harmonic analysis if often concerned with norm estimates of various operators. In contrast, probability theory usually deals with estimates on the distribution function. Probabilists' viewpoint seems more reasonable to us. We show that some important operators (such as "Triangular Truncation" or "Martingale Transform") allow the distributional estimate via Calderon operator (and this is optimal). Furthermore, recent breakthrough provides a distributional estimate for Marcinkiewicz Fourier multipliers. This sheds an additional light onto mysterious L_p-estimate due to Bourgain.

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