For a convex cocompact Fuchsian group of the second kind, a Carleson condition on the free edges of the Dirichlet domain is claimed to imply the induced measure is a Carleson measure on the whole disk.
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On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups
For a convex cocompact Fuchsian group of the second kind, a Carleson condition on the free edges of the Dirichlet domain is claimed to imply the induced measure is a Carleson measure on the whole disk.