Equivalence of Besov spaces on p.c.f. self-similar sets

Abstract

On p.c.f. self-similar sets, of which the walk dimensions of heat kernels are in general larger than 2, we find a sharp region where two classes of Besov spaces, the heat Besov spaces B p,q σ (K) and the Lipschitz-Besov spaces Λ p,q σ (K), are identitical. In particular, we provide concrete examples that B p,q σ (K) = Λ p,q σ (K) with σ > 1. Our method is purely analytical, and does not involve any heat kernel estimate.