063 Loredana Lanzani

The Cauchy-Szegö projection and its commutator for domains in C^n with minimal smoothness // Abstract:// Let $D\subset\C^n$ be a bounded, strongly pseudoconvex domain whose boundary $bD$ satisfies the minimal regularity condition of class $C^2$. A 2017 result of Lanzani and Stein states that the Cauchy-Szegö projection $S_\omega$ defined with respect to any Leray Levi-like measure $\omega$ is bounded in $L^p(bD, \omega)$ for any $1 < p < \infty$. (For this class of domains, induced Lebesgue measure is Leray Levi-like.) Here we show that $S_\omega$ is in fact 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 and $\psi_p$ is any Muckenhoupt $A_p$-weight. As an application, we characterize boundedness and compactness in $L^p(bD, \Omega_p)$ for any $1 < p < \infty$ and for any $A_p$ measure $\Omega_p$, of the commutator $[b, S_p]$ for any ...