Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

$Lip\alpha$ harmonic approximation on closed sets

Author(s): A. Bonilla; J. C. Fariña
Journal: Proc. Amer. Math. Soc. 129 (2001), 2741-2752.
MSC (2000): Primary 31A05; Secondary 30E10
Posted: 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.

References:

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