$L^p$-Boundedness of the Covariant Riesz Transform on Differential Forms for $p>2$
Differential Geometry
2025-11-17 v1
Abstract
The -boundedness for 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 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}
}