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

  • Aobo Chen

    Tsinghua University, Beijing, P. R. China
    ORCID

  • Jin Gao

    Hangzhou Normal University, P. R. China
    ORCID

  • Zhenyu Yu

    National University of Defense Technology, Changsha, P. R. China
    ORCID

  • Junda Zhang

    South China University of Technology, Guangzhou, P. R. China
    ORCID
Besov–Lipschitz norm and $p$-energy measure on scale-irregular Vicsek sets cover
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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 characterization of p-energy norms in terms of Besov–Lipschitz norms, with their weak monotonicity and the corresponding Bourgain–Brezis–Mironescu convergence.

Cite this article

Aobo Chen, Jin Gao, Zhenyu Yu, Junda Zhang, Besov–Lipschitz norm and -energy measure on scale-irregular Vicsek sets. J. Fractal Geom. (2025), published online first

DOI 10.4171/JFG/176