The Bergman projection in Lp for domains with minimal smoothness

Abstract

Let $D\subset {\mathbb{C}}^n$ be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove $L^p(D)$-regularity for the Bergman projection $B$, and for the operator $|B|$ whose kernel is the absolute value of the Bergman kernel with $p$ in the range $(1,+\mathrm{\infty })$. As an application, we show that the space of holomorphic functions in a neighborhood of $\bar{D}$ is dense in $\vartheta L^p(D)$.