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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
a.boussejra@gmail.com



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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