Harmonic Bergman functions on the unit ball in \(\mathbb R^n\) (Q1586328)

The authors study harmonic Bergman functions on the unit ball \(B\) in \(\mathbb R^n\) and show that for the Bergman kernel \(K_\alpha(x,y)\) of the orthogonal projection of \(L^{2,\alpha-1}\) onto the harmonic Bergman space \(\ell^{2,\alpha-1}\) one has the estimation \[ |K_\alpha(x,y)|= O(|x-y|^{-n+1-\alpha}) \] for \(x\in B\) and \( y\in \partial B\). Also, they calculate the duals of \({\ell}^{p,\alpha-1}\) for all \(p>0\) and \(\alpha>0\).