Lp-Liouville property for non-local operators

Jun Masamune, Toshihiro Uemura

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The Lp-Liouville property of a non-local operator A is investigated via the associated Dirichlet form (ε, F). We will show that any non-negative continuous ε-subharmonic function f ∈ Floc ∩ Lp are constant under a quite mild assumption on the kernel of ε if p ≥ 2. On the contrary, if 1 < p < 2, we need an additional assumption: either, the kernel has compact support; or f is Hölder continuous.

Original languageEnglish
Pages (from-to)2249-2267
Number of pages19
JournalMathematische Nachrichten
Volume284
Issue number17-18
DOIs
Publication statusPublished - 2011 Dec

Keywords

  • Derivation property
  • Jump process
  • Liouville property
  • Non-local operator

ASJC Scopus subject areas

  • Mathematics(all)

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