A property of purely hyperbolic Fuchsian groups of the second kind

Let $G$ be a purely hyperbolic finitely generated non-elementary Fuchsian group of the second kind. If $\Lambda$ is the limit set of the group $G$, then the function $\log(\mathrm{dist}\,(x,\Lambda))$ belongs to the class BMO. This follows from the fact that $\Lambda$ is porous, which is proved in the paper.