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arXiv · 2212.10023

Covariant Riesz transform on differential forms for $1<p\leq2$

Li-Juan Cheng·Anton Thalmaier·Feng-Yu Wang
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Abstract

In this paper, we study $L^p$-boundedness ($1<p\leq 2$) 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 Weitzenb\"{o}ck curvature endomorphism. As an application, the Calder\'on-Zygmund inequality for $1< p\leq 2$ on weighted manifolds is derived under the curvature-dimension condition as hypothesis.

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Li-Juan Cheng, Anton Thalmaier, Feng-Yu Wang. 2022-12-20. Covariant Riesz transform on differential forms for $1<p\leq2$. https://arxiv.org/abs/2212.10023

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