























Abstract:We establish the \(L^p\)-boundedness, for \(p>2\), of the covariant Riesz transform \(\nabla(\Delta_\mu^{(k)}+\sigma)^{-1/2} \) on differential forms over a class of complete weighted Riemannian manifolds. The proof is based on an heat-kernel criterion involving local volume doubling, heat kernel upper estimates, Kato-type curvature control, and gradient bounds for the heat semigroup on forms. Under curvature-dimension assumptions and Kato-type curvature bounds, this criterion applies and yields boundedness for all sufficiently large \(\sigma\). In particular, in the unweighted case, the result confirms a conjecture of Baumgarth, Devyver and Güneysu~\cite{BDG-23}. As an application, we obtain Calderón--Zygmund inequalities for \(p>2\) on weighted manifolds, which extends the recent work \cite{CCT} on manifolds without weight.
From: Li-Juan Cheng [view email]
[v1]
Fri, 14 Nov 2025 03:21:33 UTC (25 KB)
[v2]
Tue, 23 Jun 2026 02:05:25 UTC (26 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。