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arXiv · 1201.3493

Poincaré Inequality and Hajlasz-Sobolev spaces on nested fractals

Katarzyna Pietruska-Pałuba·Andrzej Stos
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Abstract

Given a nondegenerate harmonic structure, we prove a Poincaré-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.

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BibTeXRIS

Katarzyna Pietruska-Pałuba, Andrzej Stos. 2012-01-17. Poincaré Inequality and Hajlasz-Sobolev spaces on nested fractals. https://arxiv.org/abs/1201.3493

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