报告题目：Sharp weighted norm estimates for martingale square functions

报告人：吴恋  教授 （中南大学）

报告时间：2026年4月27日15：30—16：20

报告地点：腾讯会议 672217743

校内联系人：朱传喜教授     联系方式：84708351-8420

报告摘要：This paper is devoted to the study of quantitative weighted norm estimates for martingale square functions in both scalar-weighted and matrix-weighted settings. In particular, we introduce the martingale square functions $S_W$ via matrix weights $W$, and then use the matrix $A_p$ condition, introduced in our previous work, to characterize the $L_p$ estimate for $S_W$. Our proof mainly relies on the idea of sparse dominations, which leads to the explicit information on the characteristic of the matrix weight involved. For the range $1< p< 2$, our result is sharp in terms of the characteristic of the matrix weight. With some modification on the arguments, we can further improve the result in scalar settings by obtaining the optimal exponent of the characteristic of the weight involved for all indices $1 < p < 1$, addressing a fundamental problem from the classical martingale theory.

报告人简介：吴恋，中南大学教授，博导，入选国家级人才。主要研究方向为非交换分析，成果发表于J. Eur. Math. Soc., Adv. Math., Math. Ann., AOP, Trans AMS, JFA等。