On the convergence of boundary points for hyperbolic inner functions

Abstract

Abstract Given a hyperbolic inner function with Denjoy–Wolff point , it is well‐known that almost every point converges to under iteration of the radial extension . We provide explicit bounds for the rate of this convergence in terms of the angular derivative, holding almost surely. Our results also cover the case where the Denjoy–Wolff point is a singularity.