Growth and distortion theorems for linearly invariant families on homogeneous unit balls in Cn

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:407

Article

Hamada, H.¹  Honda, T.²  Kohr, G.³ 

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

[2] Hiroshima Inst Technol, Hiroshima 7315193, Japan

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

关键词: Affine invariance;    Close-to-convex mapping;    Convex mapping;    JB*-triple;    Linear invariance;    Pluriharmonic mapping;    Two-point distortion;   

DOI  :  10.1016/j.jmaa.2013.05.040

来源: Elsevier

【 摘 要 】

Let B be a homogeneous unit ball in X = C-n. In this paper, we obtain growth and distortion theorems for linearly invariant families F of locally biholomorphic mappings on the unit ball B with finite norm-order parallel to ord parallel to F-e,F-1. We use the Euclidean norm for the target space instead of the norm of X, because we are able to obtain lower bounds in the two-point distortion theorems for linearly invariant families on any homogeneous unit ball in C-n. We also obtain similar results for affine and linearly invariant families (A.L.I.F.s) of pluriharmonic mappings of the unit ball B into C-n. Again, in most of these results, we use the Euclidean norm for the target space, to obtain lower bounds in the two-point distortion theorems for A.L.I.F.s on B. These results are generalizations to homogeneous unit balls of recent results due to Graham, Kohr and Pfaltzgraff, the authors of this paper, and Duren, Hamada and Kohr. In the last section, we consider two-point distortion theorems for L.I.F.s and A.L.I.F.s on the unit polydisc U-n in C-n. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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