The Covariant Riesz Transforms on Riemannian Manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912980235452416 |
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| author | Han, Yongheng Wang, Bing |
| author_facet | Han, Yongheng Wang, Bing |
| contents | We establish the $L^p$-boundedness of the local covariant Riesz transform for differential forms on manifold $M$ with bounded $\|Rm\|$. Let $Δ_j$ be the Hodge Laplace operator on $j$-forms. For any $p \in (1, \infty)$ and $κ>κ_0$, we show that the operator $\nabla (Δ_j + κ)^{-1/2}$ is bounded on $L^p(M)$. Consequently, we obtain Calderón-Zygmund estimates for manifolds with bounded Riemannian curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22963 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Covariant Riesz Transforms on Riemannian Manifolds Han, Yongheng Wang, Bing Differential Geometry 42B20 58J35 46E35 We establish the $L^p$-boundedness of the local covariant Riesz transform for differential forms on manifold $M$ with bounded $\|Rm\|$. Let $Δ_j$ be the Hodge Laplace operator on $j$-forms. For any $p \in (1, \infty)$ and $κ>κ_0$, we show that the operator $\nabla (Δ_j + κ)^{-1/2}$ is bounded on $L^p(M)$. Consequently, we obtain Calderón-Zygmund estimates for manifolds with bounded Riemannian curvature. |
| title | The Covariant Riesz Transforms on Riemannian Manifolds |
| topic | Differential Geometry 42B20 58J35 46E35 |
| url | https://arxiv.org/abs/2603.22963 |