School Colloquium——Noncommutative weak-$L^\infty$ and BMO martingales
报告人：焦勇（中南大学）
时间：2023-11-10 14:00-15:00
地点：理科一号楼1114
Abstract：Bennett, DeVore and Sharpley (Ann of Math., 1981) introduced the weak analogue of the space $L^\infty$ and studied its relationship to the space of functions of bounded mean oscillation. The talk will present some recent progress in the context of functions on $\R^d$ with values in a semi-finite von Neumann algebra. This allows for the comparison of the $BMO$ norms of an operator-valued function and its decreasing rearrangement. The argument rests on a new distributional estimate for noncommutative martingales, which is of independent interest. The applications include related $BMO\to wL^\infty$ inequalities for square functions and conditional square functions, as well as corresponding versions of Stein and dual Doob estimates, which are new even for classical martingales.
报告人简介：焦勇，教授，博士生导师，国家杰出青年基金获得者；现任中南大学发展规划与团队建设处处长，教育部第八届科技委数理学部委员，中国工程概率统计学会理事长；主要研究领域非交换分析与概率；曾以第一完成人获湖南省自然科学一等奖。
