The Kohn-Laplacian and Cauchy-Szegö projection on Model Domains

Abstract

We study the Kohn-Laplacian and its fundamental solution on some model domains in ${\mathbb{C}}^{n+1}$, and further discuss the explicit kernel of the Cauchy-Szegö projections on these model domains using the real analysis method. We further show that these Cauchy-Szegö kernels are Calderón-Zygmund kernels under the suitable quasi-metric.