The Corona theorem for Denjoy domains (Q1066311)

The authors prove the famous corona theorem for the space of bounded analytic functions on any Denjoy domain, i.e. a connected open subset \(\Omega\) of the extended complex plane \({\mathcal C}^*\) such that the complement \({\mathcal C}^*\setminus \Omega\) is a subset of the real axis. The proof utilizes the symmetry of the Denjoy domain and the relations between length, harmonic measure, relative to the upper half plane, and analytic capacity of linear sets.