We focus on the study of the Schatten class membership of commutators involving singular integral operators. We utilize > martingale paraproducts and Hytönen's dyadic martingale technique to obtain sufficient conditions on the weak-type and strong-type Schatten class membership of commutators in terms of Sobolev spaces and Besov spaces respectively. We also establish the complex median method, which is applicable to complex-valued functions. We apply it to get the optimal necessary conditions on the weak-type and strong-type Schatten class membership of commutators associated with non-degenerate kernels. This is a joint work with Hao Zhang.

报告人简介 ：Zhenguo WEI received a bachelor’s degree from Harbin Institute of Technology in 2019 and a Ph.D. from the University of Franche-Comté,France, in 2024. He then carried out postdoctoral research at the Institute of Mathematical Sciences (ICMAT) in Spain. His main research interests lie in noncommutative harmonic analysis, with a focus on Schatten class properties and boundedness extensions for commutators of general singular integral operators, as well as optimal constant estimates for noncommutative Littlewood–Paley–Stein inequalities.Related results have been published in Science China Mathematics.