View article

In this paper, we investigate solutions of the hyperbolic Poisson equation , where and $$\begin{aligned} \Delta _{h}u(x)= (1-|x|^2)^2\Delta u(x)+2(n-2)\left( 1-|x|^2\right) \sum _{i=1}^{n} x_{i} \frac{\partial u}{\partial x_{i}}(x) \end{aligned}$$is the hyperbolic Laplace operator in the n-dimensional space for . We show that if and is a solution to the hyperbolic Poisson equation, then it has the representation provided that and . Here and denote Poisson and Green integrals with respect to , respectively. Furthermore, we prove that functions of the form are Lipschitz continuous.