Completeness of Spaces of Harmonic Functions under Restricted Supremum Norms
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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.
KeywordsHarmonic function Banach space accessibility
2000 MSC31B05 46E15
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- S. J. Gardiner, Harmonic Approximation, London Math. Soc. Lecture Note Series 221, Cambridge Univ. Press, Cambridge, 1995.Google Scholar