A multiplicative inequality of Riesz transform type on general Riemannian manifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915016937046016 |
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| author | Ouhabaz, El Maati |
| author_facet | Ouhabaz, El Maati |
| contents | Given any complete Riemannian manifold $M$, we prove that for every $p \in (1, 2]$ and every $ε> 0$, $$ \| \nabla f \|_p^2 \le C_ε\| Δ^{\frac{1}{2} + ε} f \|_{p}\| Δ^{\frac{1}{2} - ε} f \|_{p}.$$The estimate is dimension free. This inequality is even proved in the abstract setting of generators of sub-Markov semigroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A multiplicative inequality of Riesz transform type on general Riemannian manifolds Ouhabaz, El Maati Analysis of PDEs Classical Analysis and ODEs Functional Analysis Given any complete Riemannian manifold $M$, we prove that for every $p \in (1, 2]$ and every $ε> 0$, $$ \| \nabla f \|_p^2 \le C_ε\| Δ^{\frac{1}{2} + ε} f \|_{p}\| Δ^{\frac{1}{2} - ε} f \|_{p}.$$The estimate is dimension free. This inequality is even proved in the abstract setting of generators of sub-Markov semigroups. |
| title | A multiplicative inequality of Riesz transform type on general Riemannian manifolds |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2406.01097 |