Abstract
We determine precisely when the Bergman projections Pβ are bounded from Lebesgue spaces Lαp to weighted Bergman spaces Bαp of H-harmonic functions on the real hyperbolic ball, and verify a recent conjecture of M. Stoll. We obtain upper estimates for the reproducing kernels of the H-harmonic Bergman spaces Bα2 and their partial derivatives. We also consider the projection from L∞ to the Bloch space B of H-harmonic functions.
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