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Homogeneous subsets of a Lipschitz graph and the corona theorem. (English) Zbl 1217.30023

Author’s abstract: “This paper proves the corona theorem for domains in the complex plane bounded by thick subsets of a Lipschitz graph. The boundary \(E_0\) of these domains has a Carleson lower density
\[ \Lambda\big(B(z,r)\cap E_0\big)>\varepsilon_0 r\quad\text{for all}\quad z\in E_0\text{ and } r>0." \]

MSC:

30C85 Capacity and harmonic measure in the complex plane
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
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