Variation of Potentials in the Unit Ball of $ {\\shadC}^n$

Abstract

In this paper, we study the variation of invariant Green potentials G w in the unit ball B of $ {\\shadC}^n$ , which for suitable measures w are defined by $$ G_{\\mu}(z) = \\int_{B}G(z,w)\\, d\\mu(w), $$ where G is the invariant Green function for the Laplace-Beltrami operator ¨ j on B . The main result of the paper is as follows. Let w be a non-negative regular Borel measure on B satisfying $$ \\int_{B}(1-|w|^2)^n\\log {1 \\over (1-|w|^2)}\\, \\d\\mu(w) ] B , { z denotes the holomorphic automorphism of B satisfying { z (0) = z , { z ( z ) = 0 and ( { z { z )( w ) = w for every w ] B .