报告人：焦勇（中南大学）

时间：2021年6月25日14:30开始

腾讯会议ID:336 425 279

摘要:We propose a novel approach in noncommutative probability, which can be regarded as an analogue of good-$\lambda$ inequalities from the classical case due to Burkholder and Gundy (Acta Math. {\bf124}: 249-304, 1970). This resolves a longstanding open problem in noncommutative realm. Using this technique, we offer a new, simpler and unified approach to fundamental results in the noncommutative martingale theory, obtained earlier by Junge, Pisier, Randrianantoanina and Xu. We also present some fully new applications of good-$\lambda$ approach to noncommutative probability and noncommutative harmonic analysis, including new estimates for noncommutative martingales with tangent difference sequences and sums of tangent positive operators, as well as inequalities for differentially subordinate operators which have roots in the $L^p$-bound for the directional Hilbert transforms on free group von Neumann algebras and the $L^p$-estimate for the $j$-th Riesz transform on group von Neumann algebras. Finally, we answer an open problem raised by Junge and Xu in a very easy and convenient way. We emphasize that all the constants obtained in this paper are of optimal orders. This is a joint work with Adam Osekowski and Lian Wu.

简介:焦勇,中南大学数学与统计学院院长，中南大学“升华学者”特聘教授，博士生导师；湖南省杰青，国家优秀青年基金获得者。2009年6月博士毕业， 同时获得了武汉大学和法国弗朗什孔泰大学颁发的理学双博士学位；2009年7月进入中南大学工作；2012年5月入选中南大学“升华学者”特聘教授。主要研究方向为鞅论及其在调和分析和金融数学中的应用,非交换概率论。

邀请人：黄辉斥

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