The theorems of M. Riesz and Zygmund in several complex variables
- Resource Type
- Working Paper
- Source
- Subject
Mathematics - Complex Variables - Language
1$, there exists $C_\alpha>0$ such that $ \int_{\partial \Omega_t} \frac{\exp\left(\frac{\pi}2 |f| \right)}{(1+|f|)^\alpha}\, d\omega_{z_0,t} \le C_\alpha$ for any exhaustion $\{\Omega_t\}$ of $\Omega$ with $\Omega_t\ni z_0$, where $d \omega_{z_0,t}$ is the harmonic measure of $\Omega_t$ relative to $z_0$. Analogous results for Poletsky-Stessin-Hardy spaces on hyperconvex domains are given.