Schwarz Lemma at the Boundary for Holomorphic and Pluriharmonic Mappings Between $p$-unit Balls

Abstract

We give Schwarz lemma at the boundary for holomorphic mappings between $p$-unit ball $B_{p}^{n} \subset \mathbb{C}^{n}$ and $B_{p}^{N} \subset \mathbb{C}^{N}$, where $p \geq 2$. When $p = 2$, this result reduces to that of Liu, Chen and Pan [21] between the Euclidean unit balls, and our method is new. By generalizing pluriharmonic Schwarz lemma of Chen and Gauthier [5] from $p = 2$ to $p \geq 2$, we obtain the boundary Schwarz lemma for pluriharmonic mappings between $p$-unit balls.