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Poincaré Inequality and Hajlasz-Sobolev spaces on nested fractals

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.

preprint2012arXivOpen access
Katarzyna Pietruska-PałubaAndrzej Stos
math.FA
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Katarzyna Pietruska-PałubaAndrzej Stos

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