{
  "id": "math/0309463",
  "version": "v1",
  "published": "2003-09-29T17:41:51.000Z",
  "updated": "2003-09-29T17:41:51.000Z",
  "title": "A geometric approach to the Littlewood-Paley theory",
  "authors": [
    "Sergiu Klainerman",
    "Igor Rodnianski"
  ],
  "categories": [
    "math.AP",
    "math.CA",
    "math.DG"
  ],
  "abstract": "We develop a geometric invariant Littlewood-Paley theory for arbitrary tensors on a compact 2 dimensional manifold. We show that all the important features of the classical LP theory survive with estimates which depend only on very limited regularity assumptions on the metric. We give invariant descriptions of Sobolev and Besov spaces and prove some sharp product inequalities. This theory has being developed in connection to the work of the authors on the geometry of null hypersurfaces with a finite curvature flux condition, see \\cite{KR1}, \\cite{KR3}. We are confident however that it can be applied, and extended, to many different situations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-29T17:41:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric approach",
      "finite curvature flux condition",
      "geometric invariant littlewood-paley theory",
      "sharp product inequalities",
      "arbitrary tensors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9463K"
    }
  }
}