Norm of the Bergman projection onto the Bloch spave

Abstract

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

To appear in Journal of operator theory

References in corpus (1)

• Norm of the Bergman projection