{
  "id": "1612.06250",
  "version": "v1",
  "published": "2016-12-19T16:20:48.000Z",
  "updated": "2016-12-19T16:20:48.000Z",
  "title": "Strong boundedness, strong convergence and generalized variation",
  "authors": [
    "Muharem Avdispahić",
    "Zenan Šabanac"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "A trigonometric series strongly bounded at two points and with coefficients forming a log-quasidecreasing sequence is necessarily the Fourier series of a function belonging to all $L^{p}$ spaces, $1\\leq p < \\infty$. We obtain new results on strong convergence of Fourier series for functions of generalized bounded variation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-19T16:20:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A32",
      "26A45",
      "46A45"
    ],
    "keywords": [
      "strong convergence",
      "strong boundedness",
      "generalized variation",
      "fourier series",
      "trigonometric series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}