English

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

Functional Analysis 2025-07-18 v3

Abstract

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

Keywords

Cite

@article{arxiv.2406.00782,
  title  = {Besov-Lipschitz norm and $p$-energy measure on scale-irregular Vicsek sets},
  author = {Aobo Chen and Jin Gao and Zhenyu Yu and Junda Zhang},
  journal= {arXiv preprint arXiv:2406.00782},
  year   = {2025}
}

Comments

35 pages, 2 figures; a new section has been added