Consider the λ-Green function and the λ-Poisson kernel of a Lipschitz domain U ? Hn = {x ∈ Rn: xn 0} for hyperbolic Brownianmotion with drift. We provide several relationships that facilitate studyingthose objects and explain somewhat their nature. As an application, we yielduniform estimates for sets of the form Sa,b = {x ∈ Hn: xn a,x1 ∈ (0, b)}, a, b 0, which covers and extends existing results of thatkind.
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