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Lip α Approximation on Closed Sets with Lip α Extension

Published online by Cambridge University Press:  20 November 2018

A. Bonilla  and
J. C. Fariña
A. Bonilla
Affiliation:
Departamento de Analisis Matematico, Universidad de La Laguna, 38271 La Laguna (Tenerife), Canary Islands, Spain e-mail:JCFARINA@ULL.ES
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Abstract

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Let F be a relatively closed subset of a domain G in the complex plane. Let f be a function that is the limit, in the Lip α norm on F, of functions which are holomorphic or meromorphic on G (0 < α < 1). We prove that, under the same conditions that give Lip α-approximation (0 < α < 1 ) on relatively closed subsets of G, it is possible to choose the approximating function m in such a way that f — m can be extended to a function belonging to lip

Keywords

30E10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 23 - 33
Copyright
Copyright © Canadian Mathematical Society 1995

References

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