{
  "id": "1301.6267",
  "version": "v2",
  "published": "2013-01-26T16:26:57.000Z",
  "updated": "2015-05-18T18:50:44.000Z",
  "title": "The class Bp for weighted generalized Fourier transform inequalities",
  "authors": [
    "Chokri Abdelkefi",
    "Mongi Rachdi"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:1312.3744 by other authors",
  "categories": [
    "math.FA"
  ],
  "abstract": "In the present paper, we prove for the Dunkl transform which generalizes the Fourier transform, weighted inequalities when the weights belong to the well known class Bp. As application, we obtain for power weights Pitt's inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-26T16:26:57.000Z",
      "title": "The Bp condition for Weighted inequalities in Dunkl analysis and some applications",
      "abstract": "In Dunkl theory on R^d which generalizes classical Fourier analysis, we prove weighted inequalities for the Dunkl transform when the weights belong to the well-known class B_p. This result is applied to derive for power weights Pitt's theorem on R^d which gives an integrability theorem for this transform on a suitable Besov-type space.",
      "comment": "arXiv admin note: text overlap with arXiv:1208.5034",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-05-18T18:50:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10",
      "46E30",
      "44A35"
    ],
    "keywords": [
      "weighted inequalities",
      "dunkl analysis",
      "bp condition",
      "power weights pitts theorem",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.6267A"
    }
  }
}