ON KIGAMI’S CONJECTURE OF THE EMBEDDING Wp(K) ⊂ C(K)

Shiping Cao; Zhen Qing Chen; Takashi Kumagai

doi:10.1090/proc/16779

ON KIGAMI’S CONJECTURE OF THE EMBEDDING W^p(K) ⊂ C(K)

Shiping Cao
, Zhen Qing Chen
, Takashi Kumagai

University of Washington
Waseda University

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

Let (K, d) be a connected compact metric space and p ∈ (1, ∞). Under the assumption of Kigami [Conductive homogeneity of compact metric spaces and construction of p-energy, Memoirs of the European Mathematical Society, vol. 5, Europea Mathematical Society (EMS), Berline, 2023, Assumption 2.15] and the conductive p-homogeneity, we show that W^p(K) ⊂ C(K) holds if and only if p > dim_AR(K, d), where W^p(K) is Kigami’s (1, p)-Sobolev space and dim_AR(K, d) is the Ahlfors regular dimension.

源语言	英语
页（从-至）	3393-3402
页数	10
期刊	Proceedings of the American Mathematical Society
卷	152
期	8
DOI	https://doi.org/10.1090/proc/16779
出版状态	已出版 - 1 8月 2024
已对外发布	是

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引用此

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title = "ON KIGAMI{\textquoteright}S CONJECTURE OF THE EMBEDDING Wp(K) ⊂ C(K)",

abstract = "Let (K, d) be a connected compact metric space and p ∈ (1, ∞). Under the assumption of Kigami [Conductive homogeneity of compact metric spaces and construction of p-energy, Memoirs of the European Mathematical Society, vol. 5, Europea Mathematical Society (EMS), Berline, 2023, Assumption 2.15] and the conductive p-homogeneity, we show that Wp(K) ⊂ C(K) holds if and only if p > dimAR(K, d), where Wp(K) is Kigami{\textquoteright}s (1, p)-Sobolev space and dimAR(K, d) is the Ahlfors regular dimension.",

keywords = "Dirichlet form, Mosco convergence, Sierpi{\'n}ski carpets, conductance, energy measure, extension operator, harmonic function, weak convergence",

author = "Shiping Cao and Chen, \{Zhen Qing\} and Takashi Kumagai",

note = "Publisher Copyright: {\textcopyright} 2024 by the authors.",

year = "2024",

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day = "1",

doi = "10.1090/proc/16779",

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T1 - ON KIGAMI’S CONJECTURE OF THE EMBEDDING Wp(K) ⊂ C(K)

AU - Cao, Shiping

AU - Chen, Zhen Qing

AU - Kumagai, Takashi

PY - 2024/8/1

Y1 - 2024/8/1

N2 - Let (K, d) be a connected compact metric space and p ∈ (1, ∞). Under the assumption of Kigami [Conductive homogeneity of compact metric spaces and construction of p-energy, Memoirs of the European Mathematical Society, vol. 5, Europea Mathematical Society (EMS), Berline, 2023, Assumption 2.15] and the conductive p-homogeneity, we show that Wp(K) ⊂ C(K) holds if and only if p > dimAR(K, d), where Wp(K) is Kigami’s (1, p)-Sobolev space and dimAR(K, d) is the Ahlfors regular dimension.

AB - Let (K, d) be a connected compact metric space and p ∈ (1, ∞). Under the assumption of Kigami [Conductive homogeneity of compact metric spaces and construction of p-energy, Memoirs of the European Mathematical Society, vol. 5, Europea Mathematical Society (EMS), Berline, 2023, Assumption 2.15] and the conductive p-homogeneity, we show that Wp(K) ⊂ C(K) holds if and only if p > dimAR(K, d), where Wp(K) is Kigami’s (1, p)-Sobolev space and dimAR(K, d) is the Ahlfors regular dimension.

KW - Dirichlet form

KW - Mosco convergence

KW - Sierpiński carpets

KW - conductance

KW - energy measure

KW - extension operator

KW - harmonic function

KW - weak convergence

UR - https://www.scopus.com/pages/publications/85192856279

U2 - 10.1090/proc/16779

DO - 10.1090/proc/16779

M3 - Article

AN - SCOPUS:85192856279

SN - 0002-9939

VL - 152

SP - 3393

EP - 3402

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 8

ER -

ON KIGAMI’S CONJECTURE OF THE EMBEDDING Wp(K) ⊂ C(K)

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ON KIGAMI’S CONJECTURE OF THE EMBEDDING W^p(K) ⊂ C(K)