The Bergman projection in $L^{p}$ 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 $(1,+\infty)$. As an application, we show that the space of holomorphic functions in a neighborhood of $\overline{D}$ is dense in $\vartheta L^{p}(D)$.