A Julia-Wolff-Carathéodory theorem for infinitesimal generators in the unit ball (Q2790700)

Let \(\Delta \subset \mathbb C\) be the unit disk. The authors discuss the problem of generalization of the classical Julia-Wolff-Carathédory theorem for bounded holomorphic functions \(f : \Delta \rightarrow \Delta\) (see, e.g. [\textit{R. B. Burckel}, An introduction to classical complex analysis. Vol. 1. New York, San Francisco: Academic Press (1979; Zbl 0434.30002)]). In particular, they give a detailed proof of an extension of the theorem to the case of holomorphic self-maps of the unit ball in \(\mathbb C^n\) using results obtained in [\textit{F. Bracci} and \textit{D. Shoikhet}, Trans. Am. Math. Soc. 366, No. 2, 1119--1140 (2014; Zbl 1337.32016)].