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arXiv · 2003.03706

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

Shiping Cao·Hua Qiu
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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 $B^{p,q}_\sigma(K)$ and the Lipschitz-Besov spaces $\Lambda^{p,q}_\sigma(K)$, are identitical. 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 any heat kernel estimate.

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Shiping Cao, Hua Qiu. 2020-03-08. Equivalence of Besov spaces on p.c.f. self-similar sets. https://doi.org/10.4153/s0008414x23000330

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