On Hardy-Littlewood-Sobolev estimates for degenerate Laplacians
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917412409966592 |
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| author | Auscher, Pascal Baadi, Khalid |
| author_facet | Auscher, Pascal Baadi, Khalid |
| contents | We establish norm inequalities for fractional powers of degenerate Laplacians, with degeneracy being determined by weights in the Muckenhoupt class $A_2(\mathbb{R}^n)$, accompanied by specific additional reverse Hölder assumptions. This extends the known results for classical Riesz potentials. The approach is based on size estimates for the degenerate heat kernels. The approach also applies to more general weighted degenerate operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hardy-Littlewood-Sobolev estimates for degenerate Laplacians Auscher, Pascal Baadi, Khalid Analysis of PDEs Classical Analysis and ODEs Functional Analysis Primary: 46E35, 35K08, 42B37 Secondary: 35K65, 42B20 We establish norm inequalities for fractional powers of degenerate Laplacians, with degeneracy being determined by weights in the Muckenhoupt class $A_2(\mathbb{R}^n)$, accompanied by specific additional reverse Hölder assumptions. This extends the known results for classical Riesz potentials. The approach is based on size estimates for the degenerate heat kernels. The approach also applies to more general weighted degenerate operators. |
| title | On Hardy-Littlewood-Sobolev estimates for degenerate Laplacians |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis Primary: 46E35, 35K08, 42B37 Secondary: 35K65, 42B20 |
| url | https://arxiv.org/abs/2506.20368 |