THE MEAN-VALUE PROPERTY AND (α,β)-HARMONICITY

In this article we consider whether, for integrable functions on the unit ball of ℂn, the mean-value property implies (α,β)-harmonicity. We find that the answer is affirmative when 0<n+α+β≤ρ0, but is negative when n+α+β>ρ0. Here ρ0 is a constant between 11.025 and 11.069.