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 points where the function f has finite Carathéodory angular derivative 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 t
