Norm of the Bergman projection onto the Bloch spave

We consider weighted Bergman projection $P_α: L^{\infty}(\Bbb B) \rightarrow {\cal B}$ where $α>-1$ and $\cal B$ is the Bloch space of the unit ball $\Bbb B$ of the complex space $\Bbb C^n.$ We obtain the exact norm of the operator $P_α$ where the Bloch space is observed as a space with norm (and semi-norm) induced from the Besov space $B_{p},0<p<\infty,(B_{\infty}=\cal B).$ Our work contains, as a special case, the main results from \cite{Kalaj} and \cite{Ant}.

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