学术报告（李冀 1.6）

Let $D\subset\mathbb C^n$ be a bounded, strongly pseudoconvex domain whose boundary $bD$ satisfies the minimal regularity condition of class $C^2$.  We show that the Cauchy--Szeg\H o projection $S_\omega$ defined with respect to any Leray Levi-like measure $\omega$ is bounded in $L^p(bD, \Omega_p)$ for any $1 < p < \infty$ and for any $\Omega_p$ in the optimal class of $A_p$ measures, that is $\Omega_p = \psi_p\sigma$ where $\sigma$ is induced Lebesgue measure on $bD$ and $\psi_p$ is any Muckenhoupt $A_p$-weight. We then establish the characterization of boundedness and compactness of the commutator $[b, S_\omega]$ in $L^p(bD, \Omega_p)$ for any $1 < p < \infty$ and for any $A_p$ measure $\Omega_p$. We further explore the case of $S_{\Omega_2}$ and $[b,S_{\Omega_2}]$ for any $\Omega_2$ in the $A_2$ class, but the $A_p$ analogous ($1<p<\infty, p\not=2$) remains open. This is joint work with Duong, Lanzani and Wick.