Homogeneous subsets of a Lipschitz graph and the Corona Theorem

This paper proves the Corona Theorem to be affirmative for domains in the complex plane bounded by thick subsets of a Lipschitz graph. Specifically, the boundary of these domains E₀ has a Carleson lower density: ∧ ( B(z, r) ∩ E_{0) >} є ₀^r for all z ∈ E_{0 and all r >} 0.