  We solve the Dirichlet problem $\left.u\right|_{\mathbb{B}^n}=\varphi,$ for
hyperbolic Poisson's equation $\Delta_h u=\mu$ where $\varphi\in L_1(\partial
\mathbb{B}^n)$ and $\mu$ is a measure that satisfies a growth condition.
  Next we present a short proof for Lipschitz continuity of solutions of
certain hyperbolic Poisson's equations, previously established at
\cite{ChenRas}.
  In addition, we investigate some alternative assumptions on hyperbolic
Laplacian, which are connected with Riesz's potential. Also, local H\"{o}lder
continuity is proved for solution of certain hyperbolic Poisson's equations.
  We show that, if $u$ is hyperbolic harmonic in the upper half-space, then
$\frac{\partial u}{\partial y}(x_0,y)\to 0, y\to 0^+$, when boundary function
$f$ of the functions $u$ is differentiable at the boundary point $x_0$. As a
corollary, we show $C^1(\overline{\mathbb{H}^n})$ smoothness of a hyperbolic
harmonic function, which is reproduced from the $C_c^1(\mathbb{R}^{n-1})$
boundary values.
