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

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