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

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.

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

Cited by in corpus (1)

• Construction of $p$-energy measures associated with strongly local $p$-energy forms