报告人：杨福林（哈尔滨工业大学数学研究院）

时 间：2024年5月11日16:00

地 点：海韵园实验楼205报告厅

内容摘要:

In this talk, we introduce the characterisation of the Schatten properties of  $[M_b,T]$, the commutator of Calderón-Zygmund singular integral $T$ with symbol $b(M_bf(x)=b(x)f(x))$ 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 $B_p^{\Q / p}$ of the function $b$; but when $p \leq \Q$, the commutator belongs to 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 of Heisenberg groups, respectively, and hence can be applied to various setting beyond.

个人简介：

杨福林，哈尔滨工业大学数学研究院博士。2020年硕士毕业于伟德国际1946源自英国。主要研究方向是非交换分析，李群上的分析。

联系人：杨东勇