Geodesic
Boundary Behavior of Poisson Integrals on Boundaries of Symmetric Spaces
Journal of Lie theory, Tome 21 (2011) no. 2, pp. 243-261 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 43A15, 43A85
Mots-clés : Poisson integrals, Hardy-type spaces, Fatou-type theorem 
@article{JLT_2011_21_2_JLT_2011_21_2_a0,
     author = {A. Boussejra },
     title = {Boundary {Behavior} of {Poisson} {Integrals} on {Boundaries} of {Symmetric} {Spaces}},
     journal = {Journal of Lie theory},
     pages = {243--261},
     year = {2011},
     volume = {21},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2011_21_2_JLT_2011_21_2_a0/}
}
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A. Boussejra . Boundary Behavior of Poisson Integrals on Boundaries of Symmetric Spaces. Journal of Lie theory, Tome 21 (2011) no. 2, pp. 243-261. http://geodesic.mathdoc.fr/item/JLT_2011_21_2_JLT_2011_21_2_a0/