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arXiv · 2010.06776

On Carleson Measures of Beltrami Coefficients Being Compatible with Infinitely Generated Fuchsian Groups Related to Denjoy Domian

Shengjin Huo
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Abstract

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.

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Shengjin Huo. 2020-10-14. On Carleson Measures of Beltrami Coefficients Being Compatible with Infinitely Generated Fuchsian Groups Related to Denjoy Domian. https://doi.org/10.1007/s00013-018-1151-7

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