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November 2008 Evans potentials and the Riesz decomposition
Mitsuru Nakai
Hiroshima Math. J. 38(3): 455-469 (November 2008). DOI: 10.32917/hmj/1233152782

Abstract

A superharmonic function $u$ on a parabolic Riemannian manifold $M$ is shown to admit the Riesz decomposition $u=h+(1/c_{d})\int_{M}e(\cdot,y)d\mu(y)$ on $M$ into the harmonic function $h$ on $M$ and the Evans potential of an Evans kernel $e(x,y)$ on $M$ and of the Borel measure $\mu:=-\Delta u\geqq 0$ on $M$ multiplied by a certain constant $1/c_{d}$ if and only if $m(t^{2},u)-2m(t,u)={\cal O}(1)\ (t\rightarrow+\infty)$, where $m(t,u)$ is the spherical mean over the sphere of radius $t$ all induced by the above chosen Evans kernel $e(x,y)$ on $M$.

Citation

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Mitsuru Nakai. "Evans potentials and the Riesz decomposition." Hiroshima Math. J. 38 (3) 455 - 469, November 2008. https://doi.org/10.32917/hmj/1233152782

Information

Published: November 2008
First available in Project Euclid: 28 January 2009

zbMATH: 1175.31002
MathSciNet: MR2477754
Digital Object Identifier: 10.32917/hmj/1233152782

Subjects:
Primary: 31B05
Secondary: 31B15, 31C12

Rights: Copyright © 2008 Hiroshima University, Mathematics Program

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Vol.38 • No. 3 • November 2008
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