# 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} }

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.

## 7 Citations

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