广州数学大讲坛第十期
第九十八讲——中南大学吴恋副教授学术报告
题目：Noncommutative weak-$L^\infty$ and BMO
时间：2023年11月20日（星期一）上午11：00——13：00
地点：腾讯会议（会议ID：252-603-354）
报告人：吴恋副教授
摘要：Bennett, DeVore and Sharpley (Ann of Math. {\bf{113}}: 601-611, 1981) introduced the weak analogue of the space $L^\infty$ and studied its relationship to the space of functions of bounded mean oscillation. The purpose of this paper is to continue this line of research in the context of functions on $\R^d$ with values in a semifinite von Neumann algebra. As a by-product, 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 invoking Cuculescu projections, 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：
吴恋，中南大学副教授，博士生导师，主持国家自然科学基金面上和青年项目，主要从事非交换分析方向的研究，代表性论文发表于《Adv. Math.》《AOP》《CMP》《Trans. AMS》《JFA》等。
