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

Authors

  • Shengjin Huo Tiangong University, Department of Mathematics

Keywords:

Fuchsian group, Carleson measure, Ruelle's property

Abstract

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.

 

Section
Articles

Published

2021-06-21

How to Cite

Huo, S. (2021). On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups. Annales Fennici Mathematici, 46(1), 67–77. Retrieved from https://afm.journal.fi/article/view/109396