NORM OF THE BERGMAN PROJECTION ONTO THE BLOCH SPACE

We consider the weighted Bergman projection P-alpha : L-infinity (B) -> B where alpha > -1 and B is the Bloch space of the unit ball B of the complex space 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 < infinity, (B-infinity = B). As a special case of our main result we obtain the main results from D. Kalaj, M. Markovic, Norm of the Bergman projection, Math Scand., to appear, and A. Perala, On the optimal constant for the Bergman projection onto the Bloch space, Ann. Acad. Sci. Fenn. Math. 37(2012), 245-249.