{
  "id": "1511.05702",
  "version": "v1",
  "published": "2015-11-18T09:26:02.000Z",
  "updated": "2015-11-18T09:26:02.000Z",
  "title": "Algebras of singular integral operators with kernels controlled by multiple norms",
  "authors": [
    "Alexander Nagel",
    "Fulvio Ricci",
    "Elias M. Stein",
    "Stephen Wainger"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The purpose of this paper is to study algebras of singular integral operators on $\\mathbb{R}^{n}$ and nilpotent Lie groups that arise when one considers the composition of Calder\\'on-Zygmund operators with different homogeneities, such as operators that occur in sub-elliptic problems and those arising in elliptic problems. For example, one would like to describe the algebras containing the operators related to the Kohn-Laplacian for appropriate domains, or those related to inverses of H\\\"ormander sub-Laplacians, when these are composed with the more standard class of pseudo-differential operators. The algebras we study can be characterized in a number of different but equivalent ways, and consist of operators that are pseudo-local and bounded on $L^{p}$ for $1<p<\\infty$. While the usual class of Calder\\'on-Zygmund operators is invariant under a one-parameter family of dilations, the operators we study fall outside this class, and reflect a multi-parameter structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-18T09:26:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular integral operators",
      "multiple norms",
      "calderon-zygmund operators",
      "study fall outside",
      "nilpotent lie groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151105702N"
    }
  }
}