EQUIVALENCE OF BESOV SPACES ON P.C.F. SELF-SIMILAR SETS

Abstract On post-critically finite self-similar sets, whose walk dimensions of diffusions are in general larger than 2, we find a sharp region where two classes Besov spaces, the heat spaces $B^{p,q}_\sigma (K)$ and Lipschitz–Besov $\Lambda ^{p,q}_\sigma , identical. In particular, provide concrete examples that (K)=\Lambda with $\sigma>1$ . Our method is purely analytical, does not involve kernel estimate.