Abstract
We study harmonic Bergman functions on the unit ball B in Rn. Among our main results are: For the Bergman kernel Kα(x, y) of the orthogonal projection Pα of L2,α-1 onto the harmonic Bergman space l2,α-1 the following estimate holds: $$\left| {K_\alpha (x,y)} \right| = O\left( {\left| {x - y} \right|^{ - n + 1 - \alpha } } \right),{\text{ }}x \in B,{\text{ }}y \in \partial B$$ . The Bergman projection Pα is bounded for the range 1 0 and α > 0.
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