A sharp constant for the Bergman projection

Abstract

For the Bergman projection operator $P$ we prove that $\Vert P{\Vert }_{L^1(B,d\lambda )\to B_1}=\frac{(2n+1)!}{n!}.$ Here $\lambda$ stands for the invariant metric in the unit ball $B$ of ${\mathbf{C}}^n$, and $B_1$ denotes the Besov space with an adequate semi--norm. We also consider a generalization of this result. This generalizes some recent results due to Perälä.

to appear in Canadian Mathematical Bulletin