Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T00:50:28.492Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Farina, J. C., Lipschitz approximation on closed sets, J. Anal. Math. 57(1991), 152–171.Google Scholar
2. Gehring, F. W., Hayman, W. K. and Hinkkanen, A., Analytic Functions satisfying Holder conditions on the boundary, J. Approx. Theory 35(1982), 243–249.Google Scholar
3. O'Farrell, A. G., Hausdorff content and rational approximation in fractional Lipschitz norms, Trans. Amer. Math. Soc. 228(1977), 187–206.Google Scholar
4. Roth, A., Uniform and Tangential Approximation by Meromorphic functions on Closed Sets, Canad. J. Math. 28(1976), 104–111.Google Scholar
5. Roth, A., Uniform approximation by meromorphic functions on closed sets with continuous extension into the boundary, Canad. J. Math. 30(1978), 1243–1255.Google Scholar
6. Stray, A., Decomposition of approximable functions, Ann. of Math. 120(1984), 225–235.Google Scholar