Abstract
Our main result is an estimate for a sharp maximal function, which implies a Keith–
Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.
Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.
| Original language | English |
|---|---|
| Number of pages | 21 |
| Journal | arXiv.org |
| Publication status | Published - 2017 |
| MoE publication type | Not Eligible |
Keywords
- Analysis on metric spaces
- Sobolev spaces
- Poincaré inequality
- geodesic space
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Kinnunen, J., Lehrbäck, J., Vähäkangas, A. V., & Zhong, X. (2017). Maximal Function Estimates and Self-improvement Results for Poincaré Inequalities. arXiv.org. https://arxiv.org/pdf/1705.05072.pdf