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

Covariant Riesz transform on differential forms for $1<p≤2$
by Li-Juan Cheng, Anton Thalmaier and Feng-Yu Wang

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.

The paper is available here:

PDF (196K) arXiv:2212.10023

Li-Juan Cheng	chenglj@zjut.edu.cn
Anton Thalmaier	anton.thalmaier@uni.lu
Feng-Yu Wang	wangfy@tju.edu.cn

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Covariant Riesz transform on differential forms for 1<p≤2 by Li-Juan Cheng, Anton Thalmaier and Feng-Yu Wang

Covariant Riesz transform on differential forms for $1<p≤2$
by Li-Juan Cheng, Anton Thalmaier and Feng-Yu Wang