Necessary conditions for the existence of higher order extensions of univalent mappings from the disk to the ball

DOI10.1016/j.jmaa.2012.01.035zbMath1234.30012OpenAlexW2071030124MaRDI QIDQ408279

Jerry R. jun. Muir

Publication date: 29 March 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.01.035

zbMATH Keywords

biholomorphic mappingsBloch functionsLoewner chainsextension operatorsconvex and starlike mappings

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Holomorphic functions of several complex variables (32A10)

Related Items

Extension operators and automorphisms ⋮ Extensions of \(L^d\)-Loewner chains to higher dimensions ⋮ The Muir extension operator and Janowski univalent functions

Cites Work

• The roles played by order of convexity or starlikeness and the Bloch condition in the extension of mappings from the disk to the ball
• A modification of the Roper-Suffridge extension operator
• Close-to-starlike holomorphic functions of several variables
• Loewner chains and parametric representation in several complex variables
• Convex mappings on the unit ball of \(\mathbb C^ n\)
• Subordination chains and univalence of holomorphic mappings in C\(^n\)
• A class of Loewner chain preserving extension operators
• Holomorphic Maps from C n to C n
• Parametric Representation of Univalent Mappings in Several Complex Variables
• Coefficient Estimates for Univalent Functions
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