On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups

Let \(\mu\) be a Beltrami coefficient on the unit disk, which is compatible with finitely generated Fuchsian group \(G\) of second kind. In this paper we show that if \(\frac{|\mu|^{2}}{1-|z|^{2}}\,dx\,dy\) satisfies Carleson condition infinite boundary Dirichlet fundamental domain \(G\), then measure disk.