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- Title
Covariant Riesz transform on differential forms for 1<p≤2.
- Authors
Cheng, Li-Juan; Thalmaier, Anton; Wang, Feng-Yu
- Abstract
In this paper, we study L p -boundedness ( 1 < p ≤ 2 ) of the covariant Riesz transform on differential forms for a class of non-compact weighted Riemannian manifolds without assuming conditions on derivatives of curvature. We present in particular a local version of L p -boundedness of Riesz transforms under two natural conditions, namely the curvature-dimension condition, and a lower bound on the Weitzenböck curvature endomorphism. As an application, the Calderón–Zygmund inequality for 1 < p ≤ 2 on weighted manifolds is derived under the curvature-dimension condition as hypothesis.
- Subjects
DIFFERENTIAL forms; RIEMANNIAN manifolds; ENDOMORPHISMS; CURVATURE
- Publication
Calculus of Variations & Partial Differential Equations, 2023, Vol 62, Issue 9, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-023-02583-7