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arXiv · 1908.05174

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

Huo Shengjin
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Abstract

Suppose $\mu$ be a Beltrami coefficient on the unit disk, which is compatible with a convex co-compact Fuchsian group $G$ of the second kind. In this paper we show that if $\displaystyle\frac{|\mu|^{2}}{1-|z|^{2}}dxdy $ satisfies the Carleson condition on the infinite boundary boundary of the Dirichlet domain of $G$, then $\displaystyle\frac{|\mu|^{2}}{1-|z|^{2}}dxdy$ is a Carleson measure on the unit disk.

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Huo Shengjin. 2019-08-14. On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups. https://arxiv.org/abs/1908.05174

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