On the L^p-estimates of Riesz transforms on forms over complete Riemanian manifolds

2013/04/10 by Xiang-Dong Li, Xiang‐Dong Li, Li, Xiang-Dong
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Probability (math.PR) #advanced mathematical theories #math.PR

paper · pdf · doi:10.48550/arxiv.1304.3150

arXiv admin note: substantial text overlap with arXiv:1304.1168

arxiv created 2013/04/10 · openalex publication_date 2013/04/10 · arxiv updated 2013/04/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In our previous paper \citeLi2010, we proved a martingale transform representation formula for the Riesz transforms on forms over complete Riemannian manifolds, and proved some explicit L^p-norm estimates for the Riesz transforms on complete Riemannian manifolds with suitable curvature conditions. In this paper we correct a gap contained in \citeLi2010 and prove that the main result obtained in \citeLi2010 on the L^p-norm estimates for the Riesz transforms on forms remain valid. Moreover, we prove a time reversal martingale transform representation formula for the Riesz transforms on forms. Finally, we extend our approach and result to the Riesz transforms acting on Euclidean vector bundles over complete Riemannian manifolds with suitable curvature conditions.

Citations

• On the L^p-estimates for Beurling-Ahlfors and Riesz transforms on Riemannian manifolds

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