Boundary Behaviour of -Harmonic Functions and Non-Isotropic Hausdorff Measure

 In this paper we consider weighted boundary behaviour of -harmonic functions on the unit ball of . In particular, we show that a measure on the unit sphere of admits a component along the non-isotropic Hausdorff measure on that sphere and that this component gives rise to certain weighted boundary behaviour of the -harmonic extension of the original measure. (Received 24 July 2000; in revised form 10 August 2001)