Journal of Operator Theory

Volume 73, Issue 1, Summer 2015 pp. 113-126.

Norm of the Bergman projection onto the Bloch space

Authors: (1) David Kalaj, (2) Djordjije Vujadinović
Author institution: (1) Faculty of Mathematics, University of Montenegro, Podgorica, 81000, Montenegro
(2) Faculty of Mathematics, University of Montenegro, Podgorica, 81000, Montenegro

Summary: We consider the weighted Bergman projection $P_{\alpha}: L^{\infty}(\Bbb B) \rightarrow {\mathcal B} $ where $\alpha>-1$ and $\mathcal B$ 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 viewed as a space with norm (and semi-norm) induced from the Besov space $B_{p},0 < p < \infty,(B_{\infty}=\mathcal B).$ As a special case of our main result we obtain the main results from D. Kalaj, M. Marković, Norm of the Bergman projection, Math Scand., to appear, and A. Perälä, On the optimal constant for the Bergman projection onto the Bloch space, Ann. Acad. Sci. Fenn. Math. $(37)(2012)$, 245-249.

DOI: http://dx.doi.org/10.7900/jot.2013sep24.2006
Keywords: Bergman projection, Bloch space, operator norm

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