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 -energy norms and the corresponding -energy measures for scale-irregular Vicsek sets, which may lack self-similarity. We also investigate the characterizations of -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