Journal of Lie Theory

no. 2
Boundary Behavior of Poisson Integrals on Boundaries of Symmetric Spaces
Journal of Lie Theory, Volume 21 (2011) no. 2, pp. 243-261
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.
DOI: 10.5802/jolt.631
Classification: 43A15, 43A85
Keywords: Poisson integrals, Hardy-type spaces, Fatou-type theorem 
@article{JOLT_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},
     doi = {10.5802/jolt.631},
     zbl = {1214.43003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.631/}
}
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A. Boussejra. Boundary Behavior of Poisson Integrals on Boundaries of Symmetric Spaces. Journal of Lie Theory, Volume 21 (2011) no. 2, pp. 243-261. doi: 10.5802/jolt.631

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