On Kigami's conjecture of the embedding \(\mathcal{W}^p(K)\subset C(K)\)

DOI10.1090/PROC/16779zbMATH Open1544.30027MaRDI QIDQ6566387

Zhen-Qing Chen, Takashi Kumagai, Shiping Cao

Publication date: 3 July 2024

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceembeddingcompact metric space

Mathematics Subject Classification ID

Analysis on metric spaces (30L99) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Cites Work

• The construction of Brownian motion on the Sierpinski carpet
• Uniqueness of Brownian motion on Sierpiński carpets
• Dirichlet forms on fractals: Poincaré constant and resistance
• Differentiability of Lipschitz functions on metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Sobolev spaces on an arbitrary metric space
• On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Geometry and Analysis of Metric Spaces via Weighted Partitions
• Sobolev Spaces on Metric Measure Spaces
• Construction of 𝑝-energy and associated energy measures on Sierpiński carpets
• Conductive Homogeneity of Compact Metric Spaces and Construction of 𝑝-Energy
• Dirichlet forms on unconstrained Sierpinski carpets

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