From the Littlewood-Paley-Stein Inequality to the Burkholder-Gundy Inequality

Explore a 32-minute lecture by Xu Zhendong from Université de Bourgogne-Franche-Comté, presented at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the solution of a question posed by Xu regarding the order of optimal constants in the Littlewood-Paley-Stein inequality. Discover how this solution relies on constructing a special diffusion semi-group associated with a martingale, which establishes a pointwise relationship between the Littlewood G-function and the martingale square function. Learn about the application of this approach to vector-valued and noncommutative cases. Gain insights into the connection between the Littlewood-Paley-Stein inequality and the Burkholder-Gundy inequality in this advanced mathematical exploration.