报告题目：Distributional inequalities for noncommutative martingales
报 告 人：吴恋副教授（中南大学）
报告地点：腾讯会议 ID：587 303 066
报告摘要：Motivated by recent progress made for martingale inequalities in the context noncommutative $L_p$-spaces, more and more attention has been paid to exploring possible extensions of martingale inequalities for more general function spaces (such as noncommutative Lorentz spaces, noncommutative Orlicz spaces, symmetric Banach operator spaces, etc). A common feature of studying martingale inequalities in the spaces mentioned above is that one may often avoid having to deal with the distribution functions of measurable operators in question. We, therefore, directely establish distributional estimates for noncommutative martingales. Our results include distributional versions of the noncommutative Stein, dual Doob, martingale transform and Burkholder-Gundy inequalities. Most current martingale inequalities can be infferd from these distrubutional inequalities easily. Moreover, as an application, we also obtain some new martingale inequalities in symmetric quasi-Banach operator spaces and some interesting endpoint estimates. Our proof relies upon new and powerful extrapolation theorems, which are of independent interest.
报告人简介：吴恋，中南大学副教授，主要从事非交换分析方向的研究，研究成果发表于《Adv. Math.》, 《Comm. Math. Phys.》, 《Ann. Probab.》、《JFA》等。现主持1项国家自然科学青年基金，1项湖南省自然科学青年基金，1项中国博士后科学基金特别资助和1项中国博士后科学基金面上资助。