报告人：吴恋（中南大学）

时间：2023年12月02日 10:00-

地点：数统学院LD402

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.

简介：吴恋，中南大学教授，博士生导师，曾入选国家级青年人才，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。

邀请人：周国立

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