Boundary behavior of the Szegö kernel

Abstract

We give a Hörmander-type localization principle for the Szegö kernel $S_{\Omega }(z)$. We also show that for each boundary point $z_0$, $S_{\Omega }(z)\gtrsim |z-z_0{|}^{-\frac{1}{3}}$ holds non-tangentially for any bounded pseudoconvex domain with smooth boundary in ${\mathbb{C}}^2$.