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

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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 characterization of p -energy norms in terms of Besov–Lipschitz norms, with their weak monotonicity and the corresponding Bourgain–Brezis–Mironescu convergence.