论文标题
$ 1 <p \ leq2 $以差异形式变换的协变riesz变换
Covariant Riesz transform on differential forms for $1<p\leq2$
论文作者
论文摘要
在本文中，我们研究了$ l^p $结合度（$ 1 <p \ leq 2 $）的协方差riesz在一类非紧密加权的riemannian歧管上的差分形式转换，而没有假设曲率衍生物的条件。我们特别介绍了Riesz在两个自然条件下变换的本地版本，即曲率维度条件，以及Weitzenböck曲率内态的下限。作为一种应用，加权歧管上的calderón-zygmund不平等在加权歧管上以1 <p \ leq 2 $作为假设得出。
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 Weitzenböck curvature endomorphism. As an application, the Calderón-Zygmund inequality for $1< p\leq 2$ on weighted manifolds is derived under the curvature-dimension condition as hypothesis.
