Lp-Liouville Property for Non-Local Operators

2011/03/09 by Masamune, Jun, Uemura, Toshihiro · 1 citation
Mathematics · #31B05 #31C25 #42B20 (Primary) #47G20 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1103.1781

openalex publication_date 2011/03/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The Lp-Liouville property of a non-local operator A is investigated via the associated Dirichlet form. We will show that any non-negative continuous Lp E-subharmonic functions are constant under a quite mild assumption on the kernel of E if p is not less than 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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• A remark on subharmonicity for symmetric Dirichlet forms

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