Geodesic
Boundary Behavior of Poisson Integrals on Boundaries of Symmetric Spaces
Abdelhamid Boussejra1
1Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kénitra, Morocco
Journal of Lie Theory, Tome 21 (2011) no. 2, pp. 243-261

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Abdelhamid Boussejra  1

1 Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kénitra, Morocco 
Abdelhamid 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/JOLT_2011_21_2_a0/
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     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/JOLT_2011_21_2_a0/}
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