{
  "id": "math/0701939",
  "version": "v6",
  "published": "2007-01-31T19:55:36.000Z",
  "updated": "2009-07-31T15:37:17.000Z",
  "title": "Pitt's inequality and the fractional Laplacian: sharp error estimates",
  "authors": [
    "William Beckner"
  ],
  "comment": "v.6. Added new results extending estimates for fractional smoothness to the Heisenberg group and product spaces with mixed homogeneity. 25 pages, AMSLaTeX",
  "categories": [
    "math.AP"
  ],
  "abstract": "Sharp error estimates in terms of the fractional Laplacian and a weighted Besov norm are obtained for Pitt's inequality by using the spectral representation with weights for the fractional Laplacian due to Frank, Lieb and Seiringer and the sharp Stein-Weiss inequality. Dilation invariance, group symmetry on a non-unimodular group and a nonlinear Stein-Weiss lemma are used to provide short proofs of the Frank-Seiringer \"Hardy inequalities\" where fractional smoothness is measured by a Besov norm.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2009-07-31T15:37:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J70",
      "42B10",
      "35A15"
    ],
    "keywords": [
      "sharp error estimates",
      "fractional laplacian",
      "pitts inequality",
      "besov norm",
      "nonlinear stein-weiss lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1939B"
    }
  }
}