Functions with finite Dirichlet sum of order p and quasi-monomorphisms of infinite graphs
2012 ◽
Vol 207
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pp. 95-138
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AbstractIn 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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2002 ◽
Vol 9
(3)
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pp. 405-414
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1986 ◽
pp. 138-149
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2010 ◽
Vol 2010
(15)
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pp. 2903-2924
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2002 ◽
Vol 13
(02)
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pp. 209-216
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