Modified Poisson kernels on rank one symmetric spaces

Mantero, Anna Maria

doi:10.1090/S0002-9939-1979-0542087-0

Modified Poisson kernels on rank one symmetric spaces
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by Anna Maria Mantero

Proc. Amer. Math. Soc. 77 (1979), 211-217

DOI: https://doi.org/10.1090/S0002-9939-1979-0542087-0

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Abstract:

An extension is obtained to the case of a real rank one noncompact symmetric space G/K of the solution of the following problem on half-spaces: given an arbitrary continuous function $f(x)$ on ${{\mathbf {R}}^n}$, is it possible to find a function F on ${{\mathbf {R}}^n} \times {{\mathbf {R}}^ + }$ such that $F(x,y)$ is continuous for $y > 0$, harmonic for $y > 0$ and such that $F(x,0) = f(x)$?

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