𝐿𝑖𝑝𝛼 harmonic approximation on closed sets

Bonilla, A.; Fariña, J.

doi:10.1090/S0002-9939-01-05868-3

$Lip\alpha$ harmonic approximation on closed sets
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by A. Bonilla and J. C. Fariña PDF

Proc. Amer. Math. Soc. 129 (2001), 2741-2752 Request permission

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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