Boundary Behavior of Poisson Integralson Boundaries of Symmetric Spaces

摘要

In this paper we investigate the boundary behavior of LP-Poisson integrals for various boundaries of Riemannian Symmetric Spaces of the non-compact type. In particular, we show that if a function F on a Riemannian symmetric space G/K is solution of some invariant differential system associ-ated to a standard parabolic subgroup P_E of G then F is the Poisson integral of an L~p-function on the boundary component G/P_E if and only if it satisfies a Hardy type condition on a family of K-orbits.