Coefficient bounds for biholomorphic mappings which have a parametric representation
type: Item
instance of: scholarly article
title: Coefficient bounds for biholomorphic mappings which have a parametric representation
zbMATH Open document ID: 1167.32013
author: Qing-Hua Xu
author: Taishun Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-05-19T00:00:00Z
review text: Let \(\mathbb{C}^{n}\) be the space of \(n\) complex variables with respect to an arbitrary norm \(\|.\|\) and let \(B=\{z\in\mathbb{C}^{n}: \|z\|<1\}\) be the unit ball. \(H(B)\) denotes the set of all holomorphic mappings from \(B\) into \(\mathbb{C}^{n}\). Let \(S_{g}^{0}(B)\) be the class of mappings \(f\in H(B)\) which have \(g\)-parametric representation on \(B\). Denote by \(S_{g,k+1}^{0}(B)\) the subset of \(S_{g}^{0}(B)\) consisting of mappings \(f\) for which there exists a \(g\)-Loewner chain \(f(z,t)\) such that \(\{e^{-t}f(z,t)\}_{t\geq0}\) is a normal family on \(B\), \(f=f(.,0)\) and \(z=0\) is a zero of order \(k+1\) of \(e^{-t}f(z,t)-z\) for each \(t\geq0\). In the paper, the authors give coefficient bounds of mappings in \(S_{g,k+1}^{0}(B)\). These results generalize the related works of Hamada, Honda and Kohr.
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 32A10
zbMATH DE Number: 5555240
zbMATH Keywords: holomorphic mapping
zbMATH Keywords: Loewner chain
zbMATH Keywords: \(g\)-Loewner chain
zbMATH Keywords: coefficient bounds
reviewed by: Dorina Raducanu
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.01.056
OpenAlex ID: W1968438276
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DOI: 10.1016/J.JMAA.2009.01.056
description: scientific article; zbMATH DE number 5555240