  Let $\Omega$ be a Carleson-Denjoy domain and $G$ be its covering group. Let
$\mu$ be a Beltrami coefficient on the unit disk which is compatible with the
group $G$. In this paper we show that if $\frac{|\mu|^{2}}{1-|z|^{2}}dxdy$
satisfies the Carleson condition on the infinite boundary of the Dirichlet
fundamental domain of $G$, then $\frac{|\mu|^{2}}{1-|z|^{2}}dxdy$ is a Carleson
measure on the unit disk. We also show that the above property does not hold
for Denjoy domain.
