The Kohn-Laplacian and Cauchy-Szeg\"{o} 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-Szeg\"o projections on these model domains using the real analysis method. We further show that these Cauchy-Szeg\"o kernels are Calder\'on-Zygmund kernels under the suitable quasi-metric.