On the dichotomy of p-walk dimensions on metric measure spaces

2025/09/10 by Yang, Meng
#28A80 #31E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2509.08641

Abstract

On a volume doubling metric measure space endowed with a family of p-energies such that the Poincaré inequality and the cutoff Sobolev inequality with p-walk dimension β_p hold, for p in an open interval I⊆ (1,+∞), we prove the following dichotomy: either β_p=p for all p∈ I, or β_p>p for all p∈ I.

Citations

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Related

• p-Poincaré inequalities and cutoff Sobolev inequalities on metric measure spaces
• On singularity of p-energy measures on metric measure spaces
• A note on metric-measure spaces supporting Poincaré inequalities
• Poincaré inequality and energy of separating sets
• Energy inequalities for cutoff functions of p-energies on metric measures spaces