Pluriharmonic mappings in Cn and complex Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:426

Article

Hamada, Hidetaka¹  Kohr, Gabriela² 

[1] Kyushu Sangyo Univ, Fac Engn, Higashi Ku, Fukuoka 8138503, Japan

[2] Univ Babes Bolyai, Fac Math & Comp Sci, Cluj Napoca 400084, Romania

关键词: Linearly connected domain;    Pluriharmonic mapping;    Quasiconformal mapping;    Schwarz lemma;    Landau and Bloch theorems;    Univalent mapping;   

DOI  :  10.1016/j.jmaa.2015.01.052

来源: Elsevier

【 摘 要 】

In this paper, we obtain a sufficient condition for pluriharmonic mappings on the Euclidean unit ball B-n to be univalent, sense-preserving, quasiconformal and bi-Lipschitz diffeomorphisms on IL B-n and to have linearly connected images. Also, we give a sufficient condition for pluriharmonic mappings on II, B-n to have quasiconformal extensions to C-n. Next, we generalize the harmonic Schwarz lemma to pluriharmonic mappings of the unit ball B-x of a complex Banach space X into the unit ball B-n of C-n with respect to an arbitrary norm. Further, we obtain a generalization of the harmonic Schwarz-Pick lemma to the case of pluriharmonic mappings of the homogeneous unit ball Bx of a complex Banach space X into the unit ball B-n. We also obtain a version of the holomorphic Schwarz-Pick lemma for the Jacobian determinant on the Euclidean unit ball B-n to the case of pluriharmonic mappings of the homogeneous unit ball Bx into B-n, in the case that Bx is an open subset of C-n. Finally, we obtain the Landau and the Bloch theorems for pluriharmonic or holomorphic mappings on finite dimensional homogeneous unit balls. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free