Estimates of the $L^p$ norms of the Bergman projection on strongly pseudoconvex domains

We give estimates of the $L^p$ norm of the Bergman projection on a strongly pseudoconvex domain in ${\mathbb{C}}^n$. We show that this norm is comparable to $\frac{p^2}{p-1}$ for $1<p<\mathrm{\infty }$.