Abstract
In this paper, we give definitions of p-energy forms on homogenous p.c.f. self-similar sets and point that the domains of non-local p-energy form, local p-energy form are Lipschitz spaces \(B_{p, p}^{\sigma }\), \(B_{p, \infty }^{\sigma }\) respectively. By constructing equivalent semi-norms of p-energy forms, we obtain the convergence of the \(B_{p, p}^{\sigma }\)-norms to the \(B_{p, \infty }^{\sigma ^{*}}\)-norm as σ ↑ σ∗, where the critical exponent σ∗ is the supremum of σ such that \(B_{p,\infty }^{\sigma }\cap C(K)\text { is dense in }C(K)\).
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Acknowledgments
The authors were supported by National Natural Science Foundation of China (11871296). The authors thank Jiaxin Hu, Qingsong Gu, and Meng Yang for many valuable discussions.
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Gao, J., Yu, Z. & Zhang, J. Convergence of p-Energy Forms on Homogeneous p.c.f Self-Similar Sets. Potential Anal 59, 1851–1874 (2023). https://doi.org/10.1007/s11118-022-10031-y
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DOI: https://doi.org/10.1007/s11118-022-10031-y