{
  "id": "1506.01629",
  "version": "v1",
  "published": "2015-06-04T15:47:02.000Z",
  "updated": "2015-06-04T15:47:02.000Z",
  "title": "Fourier series in weighted Lorentz spaces",
  "authors": [
    "Javad Rastegari",
    "Gord Sinnamon"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The Fourier coefficient map is considered as an operator from a weighted Lorentz space on the circle to a weighted Lorentz sequence space. For a large range of Lorentz indices, necessary and sufficient conditions on the weights are given for the map to be bounded. In addition, new direct analogues are given for known weighted Lorentz space inequalities for the Fourier transform. Applications are given that involve Fourier coefficients of functions in LlogL and more general Lorentz-Zygmund spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-04T15:47:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "46E30",
      "42B05"
    ],
    "keywords": [
      "fourier series",
      "general lorentz-zygmund spaces",
      "fourier coefficient map",
      "weighted lorentz sequence space",
      "weighted lorentz space inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150601629R"
    }
  }
}