  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 $\bar{D}$ is dense in $\vartheta L^p (D)$.
