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June 2011 Harmonic morphisms applied to classical potential theory
Bent Fuglede
Nagoya Math. J. 202: 107-126 (June 2011). DOI: 10.1215/00277630-1260468

Abstract

It is shown that if φ denotes a harmonic morphism of type Bl between suitable Brelot harmonic spaces X and Y, then a function f, defined on an open set VY, is superharmonic if and only if fφ is superharmonic on φ1(V)X. The “only if” part is due to Constantinescu and Cornea, with φ denoting any harmonic morphism between two Brelot spaces. A similar result is obtained for finely superharmonic functions defined on finely open sets. These results apply, for example, to the case where φ is the projection from RN to Rn (N>n1) or where φ is the radial projection from RN{0} to the unit sphere in RN (N2).

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Bent Fuglede. "Harmonic morphisms applied to classical potential theory." Nagoya Math. J. 202 107 - 126, June 2011. https://doi.org/10.1215/00277630-1260468

Information

Published: June 2011
First available in Project Euclid: 31 May 2011

zbMATH: 1235.31002
MathSciNet: MR2804548
Digital Object Identifier: 10.1215/00277630-1260468

Subjects:
Primary: 31B05, 31C05, 31C12, 31C40

Rights: Copyright © 2011 Editorial Board, Nagoya Mathematical Journal

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Vol.202 • June 2011
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