Rate of growth of pth means of invariant potentials in the unit ball of \({\mathbb{C}}^ n\) (Q910895)

Recently, \textit{S. J. Gardiner} [Proc. Am. Math. Soc. 103, No.3, 861-869 (1988; Zbl 0672.31005)] obtained sharp results on the rate of growth of pth means of potentials on the unit ball in \({\mathbb{R}}^ n\). The author proves analogous results for Möbius invariant potentials V on the unit ball in \({\mathbb{C}}^ n\), e.g. if \(1\leq p<(2n-1)/2(n-1)\) then \[ \lim_{r\to 1-}(1-r^ 2)^{n(1-1/p)}[\int_{S}V(rt)^ p d\sigma (t)]^{1/p}=0. \]