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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2505.20555 |
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| _version_ | 1866911051249876992 |
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| author | Esmayli, Behnam Mishra, Riddhi |
| author_facet | Esmayli, Behnam Mishra, Riddhi |
| contents | We give sufficient geometric conditions, not involving capacities, for a compact null set to be removable for the Sobolev functions on weighted $\mathbb R^n$, defined as the closure of smooth functions in the weighted Sobolev norm. Our porosity conditions are in terms of suitable coverings by cubes. The weights are assumed to be doubling and satisfy a Poincaré inequality, which includes, but is not equal to, the famous class of Muckenhoupt weights. Our proofs use ideas and techniques from the theory of analysis on metric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20555 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Removable Sets for Weighted Sobolev Functions Esmayli, Behnam Mishra, Riddhi Functional Analysis Primary 46E35, Secondary 46E36 We give sufficient geometric conditions, not involving capacities, for a compact null set to be removable for the Sobolev functions on weighted $\mathbb R^n$, defined as the closure of smooth functions in the weighted Sobolev norm. Our porosity conditions are in terms of suitable coverings by cubes. The weights are assumed to be doubling and satisfy a Poincaré inequality, which includes, but is not equal to, the famous class of Muckenhoupt weights. Our proofs use ideas and techniques from the theory of analysis on metric spaces. |
| title | On Removable Sets for Weighted Sobolev Functions |
| topic | Functional Analysis Primary 46E35, Secondary 46E36 |
| url | https://arxiv.org/abs/2505.20555 |