报告题目：Schatten properties of singular integral commutators on stratified Lie groups

报告摘要：In this talk, we introduce the characterisation of the Schatten properties of $[{{M}_{b}},T]$, the commutator of Calderon-Zygmund singular integral $T$ with symbol $b$(${{M}_{b}}f(x)=b(x)f(x)$) on stratified Lie groups $G$. We show that, when $p$ is larger than the homogeneous dimension $Q$ of $G$, the Schatten ${{S}^{p}}$norm of the commutator is equivalent to the Besov semi-norm $B_{p}^{\frac{Q}{p}}$of the function $b$; but when$\text{p}\les \text{Q}$, the commutator belongs to ${{S}^{p}}$ if and only if $b$ is a constant. For the endpoint case at the critical index $p=Q$, we further show that the Schatten  ${{S}^{Q,\infty }}$ norm of the commutator is equivalent to the Sobolev norm ${{W}^{1,Q}}$ of $b$. Our method at the endpoint case differs from existing methods of Fourier transforms or trace formula for Euclidean spaces or Heisenberg groups, respectively, and hence can be applied to various settings beyond.

报告人简介：杨福林，目前就读于哈尔滨工业大学数学研究院，导师为熊枭教授，2020年硕士研究生毕业于厦门大学数学科学学院，研究生导师为伍火熊教授。主要研究兴趣是非交换分析，李群上的分析。日前被J. Math. Pures Appl. 杂志接收论文1篇。

报告时间：2024年5月17日11:00-12:00

报告地点：同析4号楼406教室