{
  "id": "1304.3150",
  "version": "v1",
  "published": "2013-04-10T21:34:57.000Z",
  "updated": "2013-04-10T21:34:57.000Z",
  "title": "On the $L^p$-estimates of Riesz transforms on forms over complete Riemanian manifolds",
  "authors": [
    "Xiang-Dong Li"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1304.1168",
  "categories": [
    "math.PR"
  ],
  "abstract": "In our previous paper \\cite{Li2010}, 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 \\cite{Li2010} and prove that the main result obtained in \\cite{Li2010} 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-10T21:34:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riesz transforms",
      "complete riemanian manifolds",
      "complete riemannian manifolds",
      "reversal martingale transform representation formula",
      "time reversal martingale transform representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.3150L"
    }
  }
}