Estimates on the Bergman Kernels in a Tangential Direction on Pseudoconvex Domains in C 3

Abstract

Let $\mathrm{\Omega }$ be a smoothly bounded pseudoconvex domain in ${\mathbb{C}}^{\mathrm{3}}$ and assume that where $z_{\mathrm{0}}\in b\mathrm{\Omega }$, the boundary of $\mathrm{\Omega }$. Then we get optimal estimates of the Bergman kernel function along some “almost tangential curve” $C_b(z_{\mathrm{0}},{\mathrm{\delta }}_{\mathrm{0}})\subset \mathrm{\Omega }\cup \left\{z_{\mathrm{0}}\right\}$.