A Sharp Entropy Condition For The Density Of Angular Derivatives
Let f be a holomorphic self-map of the unit disc. We show that if log(1−|f(z)|) is integrable on a sub-arc of the unit circle, I, then the set of Carathéodory angular derivatives of f on I is a countable union of Beurling-Carleson sets of finite entropy. Conversely, given a countable union of Beurling-Carleson sets, E, we construct a holomorphic self-map of the unit disc, such that its set of Cara
