2013/09/12 by Anastasia Frolova, Marina Levenshtein, Frolova, A. +5
Mathematics · #30c35 (Primary) #37c10 (Secondary) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1309.3074
openalex publication_date 2013/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish some estimates of the the angular derivatives from below for holomorphic self-maps of the unit disk at one and two fixed points of the unit circle provided there is no fixed point inside the unit disk. The results complement Cowen-Pommerenke and Anderson-Vasil'ev type estimates in the case of univalent functions. We use the method of extremal length and propose a new semigroup approach to deriving inequalities for holomorphic self-maps of the disk which are not necessarily univalent using known inequalities for univalent functions. This approach allowed us to receive a new Ossermans type estimate as well as inequalities for holomorphic self-maps which images do not separate the origin and the boundary.