
Journal of Lie Theory 21 (2011), No. 2, 243261 Copyright Heldermann Verlag 2011 Boundary Behavior of Poisson Integrals on Boundaries of Symmetric Spaces Abdelhamid Boussejra Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kénitra, Morocco a.boussejra@gmail.com We investigate the boundary behavior of L^{p}Poisson integrals for various boundaries of Riemannian Symmetric Spaces of the noncompact type. In particular, we show that if a function F on a Riemannian symmetric space G/K is solution of some invariant differential system associated to a standard parabolic subgroup P_{E} of G then F is the Poisson integral of an L^{p}function on the boundary component G/P_{E} if and only if it satisfies a Hardy type condition on a family of Korbits. Keywords: Poisson integrals, Hardytype spaces, Fatoutype theorem. MSC: 43A15, 43A85 [ Fulltextpdf (309 KB)] for subscribers only. 