Rate of growth of \(p\)th means of invariant potentials in the unit ball of \(\mathbb{C}{}^ n\). II
Earlier results [Part I, ibid. 143, 480-499 (1989; Zbl 0697.31008)] on the rate of growth of the means \(M_ p\) of Moebius invariant Green potentials on the unit ball \(B\) in \(\mathbb{C}^ n\) are extended. A typical result is the following: Let \(\beta\in\mathbb{R}\), \(n\leq q\leq p<\infty\) and \(f\geq 0\) such that \(\int_ B(1-| w|^ 2)^ \beta\int^ q(w)d\lambda(w)<\infty\) \((\lambda\) invariant measure on \(B\)). Let \((\beta-n)/q<\alpha<n(1-1/p)+\beta/q\) and let \(M_ p(G_ f^ \alpha,r)\) denote the \(p\)-th mean of \(G_ f^ \alpha=\int(1-| w|^ 2)^ \alpha f(w)G(\cdot,w)d\lambda(w)\) on \(\{z\in\mathbb{C}^ n:| z|=r\}\) \((G\) Moebius invariant Green function on \(B\)). Then \[ \lim_{r\to 1}(1-r^ 2)^{\beta/q-n/p-\alpha}M_ p(G^ \alpha_ f,r)=0. \]
scientific article; zbMATH DE number 60454