Geodesic
On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups
Shengjin Huo1
1 Tiangong University, Department of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 67-77

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

Shengjin Huo 1

1 Tiangong University, Department of Mathematics 
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Shengjin Huo. On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 67-77. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a4/