Abstract
In this paper, by using the invariant potential theory in the unit ball of , we give a characierization of the “Bergman ball” in terms of spherical mean–value property of m-harmonic functions. We establish a property on the normal derivaiive of the single layer m-potential in the boundary of a “regular”domain Ω of the unit ball ami we use it to prove if the average over ∂Ω of the m-potential of masses lying entirely outside Ω is equal to the value of that potential at some interior point aOf Ω, then Ω is a “Bergman ball” centered at a;.
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