Norm of the Bergman projection onto the Bloch spave

TL;DR

This paper determines the exact norm of the weighted Bergman projection from essentially bounded functions to the Bloch space on the unit ball in complex space, extending previous results and providing precise operator bounds.

Contribution

It computes the exact norm of the Bergman projection onto the Bloch space for weighted cases, generalizing earlier findings and using a specific norm structure.

Findings

Exact norm of the projection is obtained.

Results include special cases from prior studies.

Provides a precise operator norm in the context of complex analysis.

Abstract

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