Construction of convex mappings of \(p\)-balls in \(\mathbb{C}^2\)
type: Item
instance of: scholarly article
title: Construction of convex mappings of \(p\)-balls in \(\mathbb{C}^2\)
zbMATH Open document ID: 1056.32017
DOI: 10.1007/BF03321052
author: Jerry R. jun. Muir
author: Ted J. Suffridge
published in: Computational Methods and Function Theory
publication date: 2004-09-28T00:00:00Z
review text: The authors consider biholomorphic mappings \(F\) of the \(p\)-ball \(B_p=\{ (z,w)\in\mathbb{C}^2 : | z| ^p+| w| ^p < 1 \}\), where \(2\leq p < \infty\). In particular, they find conditions under which functions of the form \(F(z,w)=(z+aw^k,w)\), where \(a\in\mathbb{C}\) and \(k\in\mathbb{N}\), and \(F(z,w)=(f(z),g(w))\), where \(f\) and \(g\) are mappings of the unit disk, map \(B_p\) onto convex domains in \(\mathbb{C}^2\).
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 2104111
zbMATH Keywords: biholomorphic mapping
zbMATH Keywords: convex mapping
zbMATH Keywords: \(p\)-norm
reviewed by: Martin Chuaqui
MaRDI profile type: Publication
cites work: On the automorphisms of circular and Reinhardt domains in complex Banach spaces
cites work: Q4211223
cites work: Q4444884
cites work: Univalent mappings associated with the Roper-Suffridge extension operator
cites work: SCHWARZ'S LEMMA IN NORMED LINEAR SPACES
cites work: Homogeneous expansions of normalized biholomorphic convex mappings over \(B^ p\)
cites work: Unbounded convex mappings of the ball in \(\mathbb{C}^n\)
cites work: Linear Invariance, Order and Convex Maps in
cites work: Norm order and geometric properties of holomorphic mappings in \(\mathbb{C}^n\)
cites work: Convex mappings on the unit ball of \(\mathbb C^ n\)
cites work: Convexity properties of holomorphic mappings in ℂⁿ
cites work: Q3870023
cites work: The principle of subordination applied to functions of several variables
cites work: Starlike and convex maps in Banach spaces
cites work: Q3788526
cites work: Q5338702
description: scientific article; zbMATH DE number 2104111