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Boundary behavior of Poisson integrals on boundaries of symmetric spaces. (English) Zbl 1214.43003

It is well-known that a complex valued function on a bounded symmetric domain \(X=G/K\) satisfying the associated Hua system has an \(L^p\)-Poisson integral representation over the Shilov boundary of \(X\), if and only if it satisfies a Hardy type condition on a family of \(K\)-orbits; the paper extends this result to any boundary component of a Riemannian symmetric space of noncompact type.

MSC:

43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
43A85 Harmonic analysis on homogeneous spaces
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