Schwarz-Pick type estimates of pluriharmonic mappings in the unit polydisk

Abstract

In this paper, we will give Schwarz-Pick type estimates of arbitrary order partial derivatives for bounded pluriharmonic mappings defined in the unit polydisk. Our main results are generalizations of results of Colonna for planar harmonic mappings in [Indiana Univ. Math. J. 38: 829--840, 1989].