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$L^p$-Boundedness of the Covariant Riesz Transform on Differential Forms for $p>2$

Differential Geometry 2025-11-17 v1

Abstract

The LpL^p-boundedness for p>2p>2 of the covariant Riesz transform on differential forms is proved for a class of non-compact weighted Riemannian manifolds under certain curvature and volume growth conditions, which in particular settles a conjecture of Baumgarth, Devyver and G\"uneysu~\cite{BDG-23}. As an application, the Calder\'on-Zygmund inequality for p>2p> 2 is derived on weighted manifolds, which extends the recent work \cite{CCT} on manifolds without weight.

Keywords

Cite

@article{arxiv.2511.10922,
  title  = {$L^p$-Boundedness of the Covariant Riesz Transform on Differential Forms for $p>2$},
  author = {Li-Juan Cheng and Anton Thalmaier and Feng-Yu Wang},
  journal= {arXiv preprint arXiv:2511.10922},
  year   = {2025}
}