Israel Journal of Mathematics

, Volume 202, Issue 1, pp 475–490 | Cite as

L q harmonic functions on graphs

  • Bobo HuaEmail author
  • Jürgen Jost


We prove an analogue of Yau’s Caccioppoli-type inequality for nonnegative subharmonic functions on graphs. We then obtain a Liouville theorem for harmonic or nonnegative subharmonic functions of class L q , 1 ≤ q < ∞, on any graph, and a quantitative version for q > 1. Also, we provide counterexamples for Liouville theorems for 0 < q < 1.


Harmonic Function Edge Weight Weighted Graph Subharmonic Function Complete Riemannian Manifold 
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Copyright information

© Hebrew University of Jerusalem 2014

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Department of Mathematics and Computer ScienceUniversity of LeipzigLeipzigGermany

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