Poincar\'e Inequality and Hajlasz-Sobolev spaces on nested fractals

Given a nondegenerate harmonic structure, we prove a Poincar\'e-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajlasz-Sobolev spaces on nested fractals. In particular, we describe how the "weak"-type gradient on nested fractals...

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Bibliographic Details
Main Authors Pietruska-Pałuba, Katarzyna, Stos, Andrzej
Format Journal Article
LanguageEnglish
Published 17.01.2012
Subjects
Mathematics - Functional Analysis
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Summary:Given a nondegenerate harmonic structure, we prove a Poincar\'e-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajlasz-Sobolev spaces on nested fractals. In particular, we describe how the "weak"-type gradient on nested fractals relates to the upper gradient defined in the context of general metric spaces.
DOI:10.48550/arxiv.1201.3493