Averaging properties of pluriharmonic boundary values (Q1059747)

Suppose \(D\subset {\mathbb{C}}^ n\) is a smoothly bounded domain and u is bounded and pluriharmonic in D. let \(u^*\) denote the boundary function of u, and let \(\zeta_ 0\in \partial D\). It is shown that if \(u^*\) has good averaging behavior on one curve in \(\partial D\) through \(\zeta_ 0\), then \(u^*\) has bood averaging behavior on all curves in \(\partial D\) through \(\zeta_ 0\), provided the curves in question satisfy a certain directional condition. These results fail if the directional condition on the curve is violated.