Poincaré Inequality and Hajlasz-Sobolev spaces on nested fractals
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2012
- DOI:
- 10.48550/arXiv.1201.3493
- arXiv:
- arXiv:1201.3493
- Bibcode:
- 2012arXiv1201.3493P
- Keywords:
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- Mathematics - Functional Analysis