A Survey of the $L^p$ Regularity of the Bergman Projection

Abstract

Although the Bergman projection operator ${\mathbf{B}}_{\Omega }$ is defined on $L^2(\Omega )$, its behavior on other $L^p(\Omega )$ spaces for $p\ne 2$ is an active research area. We survey some of the recent results on $L^p$ estimates on the Bergman projection.