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Journal of Lie Theory 21 (2011), No. 2, 243--261
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, KÚnitra, Morocco

We investigate the boundary behavior of Lp-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 PE of G then F is the Poisson integral of an Lp-function on the boundary component G/PE if and only if it satisfies a Hardy type condition on a family of K-orbits.

Keywords: Poisson integrals, Hardy-type spaces, Fatou-type theorem.

MSC: 43A15, 43A85

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