Moment vanishing properties of harmonic Bergman functions ✩

We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces b p δ on the upper half-space must have the moment vanishing properties. As an application, we show that b p 0 , p 1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to b p δ .  2004 Elsevier Inc. All rights reserved.