{
  "id": "1204.1281",
  "version": "v2",
  "published": "2012-04-05T17:32:58.000Z",
  "updated": "2012-04-07T09:16:35.000Z",
  "title": "Pointwise strong and very strong approximation by Fourier series of integrable functions",
  "authors": [
    "W\\lodzimierz \\Lenski"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We will present an estimation of the $H_{k_{0},k_{r}}^{q}f$ $\\ $and $% H_{u}^{\\lambda \\varphi}f$ means as a approximation versions \\ of \\ the Totik type generalization$(\\text{see \\cite{11, 12}}) $ \\ of the results of \\ J. Marcinkiewicz and A. Zygmund in \\cite{JM, ZA}. As a measure of such approximations we will use the function constructed on the base of definition of the Gabisonia points \\cite{1}. Some results on the norm approximation will also given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-07T09:16:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strong approximation",
      "fourier series",
      "integrable functions",
      "pointwise strong",
      "totik type generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.1281L"
    }
  }
}