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September 2012 Functions with finite Dirichlet sum of order p and quasi-monomorphisms of infinite graphs
Tae Hattori, Atsushi Kasue
Nagoya Math. J. 207: 95-138 (September 2012). DOI: 10.1215/00277630-1630041

Abstract

In this paper, we study some potential theoretic properties of connected infinite networks and then investigate the space of p-Dirichlet finite functions on connected infinite graphs, via quasi-monomorphisms. A main result shows that if a connected infinite graph of bounded degrees possesses a quasi-monomorphism into the hyperbolic space form of dimension n and it is not p-parabolic for p>n1, then it admits a lot of p-harmonic functions with finite Dirichlet sum of order p.

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Tae Hattori. Atsushi Kasue. "Functions with finite Dirichlet sum of order p and quasi-monomorphisms of infinite graphs." Nagoya Math. J. 207 95 - 138, September 2012. https://doi.org/10.1215/00277630-1630041

Information

Published: September 2012
First available in Project Euclid: 26 July 2012

zbMATH: 1248.05129
MathSciNet: MR2957144
Digital Object Identifier: 10.1215/00277630-1630041

Subjects:
Primary: 05C63 , 31C20
Secondary: 53C23

Rights: Copyright © 2012 Editorial Board, Nagoya Mathematical Journal

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Vol.207 • September 2012
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