Computational Methods and Function Theory

, Volume 4, Issue 1, pp 43–45 | Cite as

Completeness of Spaces of Harmonic Functions under Restricted Supremum Norms

  • Stephen J. GardinerEmail author


Let E be a subset of a domain Ω in Euclidean space. This note verifies a conjecture of Arcozzi and Björn concerning the completeness of the space of harmonic functions u on Ω that are bounded on E, where the supremum norm is taken with respect to the restriction of u to E.


Harmonic function Banach space accessibility 

2000 MSC

31B05 46E15 


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Copyright information

© Heldermann  Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College DublinDublin 4Ireland

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