A remark on subharmonicity for symmetric Dirichlet forms

2025/06/22 by Kuwae, Kazuhiro, Lei, Rong, Marini, Ludovico
#30L15 #31C05 #31C25 #53C21 #60J46 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.17979

Abstract

We remove the local boundedness for \mathscrE_α-subharmonicity in the framework of (not necessarily strongly local) regular symmetric Dirichlet form (\mathscrE,D(\mathscrE)) with α≥0 and establish the stochastic characterization for \mathscrE-subharmonic functions without assuming the local boundedness.

Citations

• On L^p Liouville theorems for Dirichlet forms
• Lp-Liouville Property for Non-Local Operators
• Intrinsic metrics for non-local symmetric Dirichlet forms and\n applications to spectral theory
• On subhamonicity for symmetric Markov processes
• On notions of harmonicity

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