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$Lip\alpha$ harmonic approximation on closed sets


Authors: A. Bonilla and J. C. Fariña
Journal: Proc. Amer. Math. Soc. 129 (2001), 2741-2752
MSC (2000): Primary 31A05; Secondary 30E10
DOI: https://doi.org/10.1090/S0002-9939-01-05868-3
Published electronically: February 9, 2001
MathSciNet review: 1838798
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Abstract:

In this paper the $Lip\alpha$ harmonic approximation ( $0 < \alpha < \frac {1}{2}$) on relatively closed subsets of a domain in the complex plane is characterized under the same conditions given by S. Gardiner for the uniform case. Thus, the result of P. Paramonov on $Lip\alpha$ harmonic polynomial approximation for compact subsets is extended to closed sets. Moreover, the problem of uniform approximation with continuous extension to the boundary for harmonic functions and similar questions in $Lip\alpha $ harmonic approximation are also studied.


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Additional Information

A. Bonilla
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Canary Islands, Spain
Email: abonilla@ull.es

J. C. Fariña
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Canary Islands, Spain
Email: jcfarina@ull.es

DOI: https://doi.org/10.1090/S0002-9939-01-05868-3
Received by editor(s): January 30, 2000
Published electronically: February 9, 2001
Additional Notes: This work was supported in part by Consejería de Educación, Gobierno Autónomo de Canarias, Proyecto PI 1999/105.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 2001 American Mathematical Society

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