{
  "id": "1005.1492",
  "version": "v1",
  "published": "2010-05-10T11:11:47.000Z",
  "updated": "2010-05-10T11:11:47.000Z",
  "title": "Higher order Riesz transforms in the ultraspherical setting as principal value integral operators",
  "authors": [
    "Jorge J. Betancor",
    "Juan C. Fariña",
    "Lourdes Rodríguez-Mesa",
    "Ricardo Testoni"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we represent the $k$-th Riesz transform in the ultraspherical setting as a principal value integral operator for every $k\\in \\mathbb{N}$. We also measure the speed of convergence of the limit by proving $L^p$-boundedness properties for the oscillation and variation operators associated with the corresponding truncated operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-10T11:11:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "42C15"
    ],
    "keywords": [
      "principal value integral operator",
      "higher order riesz transforms",
      "ultraspherical setting",
      "th riesz transform",
      "boundedness properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1492B"
    }
  }
}