学术报告(焦勇 9.23)

Noncommutative weak-?∞ and BMO

发布人:杨晓静 发布日期:2023-09-15
主题
Noncommutative weak-?∞ and BMO
活动时间
-
活动地址
数学楼 415
主讲人
焦勇教授 中南大学
主持人
郭先平

Abstract: Bennett, DeVore and Sharpley (Ann of Math. {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.