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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
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 > n - 1, then it admits a lot of p-harmonic functions with finite Dirichlet sum of order p.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2012
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