On the Bergman projections acting on $L^{\infty }$ in the unit ball ${\mathbb{B}}_n$

Abstract

Given a weight function, we define the Bergman type projection with values in the corresponding weighted Bergman space on the unit ball ${\mathbb{B}}_n$ of ${\mathbb{C}}^n,n>1$. We characterize the radial weights such that this projection is bounded from $L^{\infty }$ to the Bloch space $\mathcal{B}$.