Harmonic Bergman functions on the unit ball in Rn

We study harmonic Bergman functions on the unit ball B in R-n Among our main results are: For the Bergman kernel K-alpha (x, y) of the orthogonal projection P-alpha of L-2,L-alpha-1 onto the harmonic Bergman space l(2,alpha-1) the following estimate holds: \K-alpha(x, y)\ = O(\x - y\(-n+1-alpha)), x is an element of B, y is an element of partial derivative B. The Bergman projection P-alpha is bounded for the range 1 < p < infinity. Also, P-alpha maps L-infinity onto the harmonic Bloch space B-infinity and C-0(B) onto the little harmonic Bloch space B-infinity. The duals of the harmonic Bergman spaces l(p,alpha-1) are calculated for all p > 0 and alpha > 0.