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Functions with finite Dirichlet sum of order p and quasi-monomorphisms of infinite graphs

Published online by Cambridge University Press:  11 January 2016

Tae Hattori  and
Atsushi Kasue
Tae Hattori
Affiliation:
Ishikawa National College of Technology, Tsubata Kahoku-gun, Ishikawa, 929-0329, Japan
Atsushi Kasue
Affiliation:
Department of Mathematics, Kanazawa University, Kanazawa, Ishikawa, 920-1192, Japan
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Abstract

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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 > n - 1, then it admits a lot of p-harmonic functions with finite Dirichlet sum of order p.

Keywords

05C6331C2053C23
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 207 , September 2012 , pp. 95 - 138
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2012

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