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Equivalence of Besov spaces on p.c.f. self-similar sets
Part of
- Classical measure theory
- Potential theory on metric spaces
Shiping Cao, Hua Qiu
Journal:

Canadian Journal of Mathematics / Volume 76 / Issue 4 / August 2024

Published online by Cambridge University Press:

26 May 2023, pp. 1109-1143

Print publication:

August 2024
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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 of Besov spaces, the heat Besov spaces $B^{p,q}_\sigma (K)$ and the Lipschitz–Besov spaces $\Lambda ^{p,q}_\sigma (K)$, are identical. In particular, we provide concrete examples that $B^{p,q}_\sigma (K)=\Lambda ^{p,q}_\sigma (K)$ with $\sigma>1$. Our method is purely analytical, and does not involve heat kernel estimate.