Equivalence of Besov spaces on p.c.f. self-similar sets
Canadian journal of mathematics, Tome 76 (2024) no. 4, pp. 1109-1143
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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.
Mots-clés :
p.c.f. self-similar sets, Besov spaces, fractal analysis, heat kernels, Sobolev spaces
Cao, Shiping; Qiu, Hua. Equivalence of Besov spaces on p.c.f. self-similar sets. Canadian journal of mathematics, Tome 76 (2024) no. 4, pp. 1109-1143. doi: 10.4153/S0008414X23000330
@article{10_4153_S0008414X23000330,
author = {Cao, Shiping and Qiu, Hua},
title = {Equivalence of {Besov} spaces on p.c.f. self-similar sets},
journal = {Canadian journal of mathematics},
pages = {1109--1143},
year = {2024},
volume = {76},
number = {4},
doi = {10.4153/S0008414X23000330},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000330/}
}
TY - JOUR AU - Cao, Shiping AU - Qiu, Hua TI - Equivalence of Besov spaces on p.c.f. self-similar sets JO - Canadian journal of mathematics PY - 2024 SP - 1109 EP - 1143 VL - 76 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000330/ DO - 10.4153/S0008414X23000330 ID - 10_4153_S0008414X23000330 ER -
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