报告人：王子鹏

时间：2025年3月06日-2025年6月12日，每周四13:00-15:00

地点：数统学院LD701

摘要：We will present a detailed introduction to martingales in Banach spaces. Most of our material is taken from Pisier’s book, which shares the same title as our lecture. Hence, we emphasize that no prior knowledge of scalar-valued martingales is assumed. The topics at least covered in our lectures include:

(1) Basic definitions and properties of Banach-valued conditional expectations.

(2) Basic inequalities, such as the hypercontractive inequality, Kahane’s inequality, and Doob’s maximal inequality.

(3) The definition of UMD spaces and their basic properties.

(4) The connection between UMD spaces and harmonic analysis, particularly the Hilbert transform.

(5) UMD spaces and martingale inequalities, such as Burkholder’s inequality and the Burkholder-Rosenthal inequality.

邀请人: 数学研究中心

欢迎广大师生积极参与！