Besov-Lipschitz norm and p-energy measure on scale-irregular Vicsek sets

2024/06/02 by Aobo Chen, Chen, Aobo, Jin Gao +5 · 2 citations
Computer Science · Mathematics · #28A80 #46E30 #46E35 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2406.00782

openalex publication_date 2024/06/02 · openalex created_date 2024/06/07 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish the existence of p-energy norms and the corresponding p-energy measures for scale-irregular Vicsek sets, which may lack self-similarity. We also investigate the characterizations of p-energy norms in terms of Besov-Lipschitz norms, with their weak monotonicity and the corresponding Bourgain-Brezis-Mironescu convergence.

Cited by

• On the dichotomy of p-walk dimensions on metric measure spaces
• Energy inequalities for cutoff functions of p-energies on metric measures spaces

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