On a conditional theorem of Littlewood for quasiregular entire functions
type: Item
instance of: scholarly article
title: On a conditional theorem of Littlewood for quasiregular entire functions
zbMATH Open document ID: 0861.30022
DOI: 10.1007/BF02835953
author: John L. Lewis
published in: Journal d'Analyse Mathématique
publication date: 1997-05-12T00:00:00Z
review text: As well-known, the theory of quasiregular maps in \(R^n\) uses a method from several mathematical disciplines such as Sobolev spaces, nonlinear PDE's, variational calculus, and potential theory. On the other hand, one of the main motivations for the theory is to generalize ``geometric'' properties of analytic functions of the plane. In the paper under review, these both aspects are apparent. The theorem in the title connects the multiplicity function and the order of an entire quasiregular mapping. The author makes skillfull use of highly technical estimates of generalized solutions of PDE's and also uses ideas from his earlier joint paper with A. Eremenko. It is noteworthy that some of the results are new even in the particular case of analytic functions.
reviewed by: M. Vuorinen
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 569434
zbMATH Keywords: quasiregular maps
zbMATH Keywords: Sobolev spaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 569434