A sharp constant for the Bergman projection

TL;DR

This paper establishes the exact norm of the Bergman projection operator from L^1 space to a Besov space in the unit ball of complex n-space, generalizing recent findings.

Contribution

It provides a precise value for the Bergman projection norm and extends previous results to a broader context.

Findings

Exact norm of the Bergman projection operator is determined.

The result generalizes recent findings by Per"{a}l"{a}.

The work applies to the unit ball in complex n-space.

Abstract

For the Bergman projection operator $P$ we prove that $ \|P\|_{{L^1(B,d\lambda)\rightarrow 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 Per\"{a}l\"{a}.