Schwarz lemma and boundary Schwarz lemma for pluriharmonic mappings

Abstract

In this paper, we first improve the boundary Schwarz lemma for holomorphic self-mappings of the unit ball $\mathbb{B}^n$,
and then we establish the boundary Schwarz lemma for harmonic self-mappings of the unit disk $\ID$ and pluriharmonic self-mappings of $\IB^n$.
The results are sharp and coincides with the classical boundary Schwarz lemma when $n=1$.