Schwarz Lemma at the Boundary on the Classical Domain of Type $$\mathcal{III}$$

Abstract

Let $$\mathcal{R}_\mathcal{III}(n)$$ be the classical domain of type $$\mathcal{III}$$ with n ≥ 2. This article is devoted to a deep study of the Schwarz lemma on $$\mathcal{R}_\mathcal{III}(n)$$ via not only exploring the smooth boundary points of $$\mathcal{R}_\mathcal{III}(n)$$ ) but also proving the Schwarz lemma at the smooth boundary point for holomorphic self-mappings of $$\mathcal{R}_\mathcal{III}(n)$$ .