A boundary Schwarz lemma for pluriharmonic mappings from the unit polydisk to the unit ball. Issue 3 (May 2018)

• Record Type: Journal Article
• Authors: LI, Ling; LI, Hongyi; ZHAO, Di
• Is Part Of: Acta mathematica scientia. Volume 38:Issue 3(2018)
• Page Start: 926
• Page End: 934
• Publication Date: 2018-05
• Subjects: Boundary Schwarz lemma -- pluriharmonic mapping -- unit polydisk -- unit ball; 32A50; Mathematical physics -- Periodicals; 530.15
• DOI: 10.1016/S0252-9602(18)30793-8
• Languages: English
• ISSNs: 0252-9602

Abstract

Abstract: In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P ( D n, B N ) is C 1 + α at z 0 ∈ E r ⊂ ∂ D n with f (0)= 0 and f ( z 0 ) = w 0 ∈ ∂ B N for any n, N ≥ 1, then there exist a nonnegative vector λ f = ( λ 1, 0, … , λ r, 0, …, 0 ) T ∈ R 2 n satisfying λ i ≥ 1 2 2 n - 1 for 1 ≤ i ≤ r such that ( D f ( z ′ 0 ) ) T w ′ 0 = diag ( λ f ) z ′ 0, where z ′ 0 and w ′ 0 are real versions of z 0 and w 0, respectively.