In this paper, we study some potential theoretic properties of connected infinite networks and then investigate the space of -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 and it is not -parabolic for , then it admits a lot of -harmonic functions with finite Dirichlet sum of order .
"Functions with finite Dirichlet sum of order and quasi-monomorphisms of infinite graphs." Nagoya Math. J. 207 95 - 138, September 2012. https://doi.org/10.1215/00277630-1630041