Lp-Liouville property for non-local operators

@article{Uemura2011LpLiouvillePF,
  title={Lp-Liouville property for non-local operators},
  author={Junji Uemura},
  journal={Mathematische Nachrichten},
  year={2011},
  volume={284},
  pages={2249-2267}
}
  • Junji Uemura
  • Published 9 March 2011
  • Mathematics
  • Mathematische Nachrichten
The Lp-Liouville property of a non-local operator is investigated via the associated Dirichlet form . We will show that any non-negative continuous -subharmonic function are constant under a quite mild assumption on the kernel of if p ≥ 2. On the contrary, if 1 < p < 2, we need an additional assumption: either, the kernel has compact support; or f is Holder continuous. 
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