{
  "id": "1412.6795",
  "version": "v1",
  "published": "2014-12-21T15:13:17.000Z",
  "updated": "2014-12-21T15:13:17.000Z",
  "title": "Hardy-Littlewood Maximal Operator And $BLO^{1/\\log}$ Class of Exponents",
  "authors": [
    "Tengiz Kopaliani",
    "Shalva Zviadadze"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "It is well known that if Hardy-Littlewood maximal operator is bounded in space $L^{p(\\cdot)}[0;1]$ then $1/p(\\cdot)\\in BMO^{1/\\log}$. On the other hand if $p(\\cdot)\\in BMO^{1/\\log},$ ($1<p_{-}\\leq p_{+}<\\infty$), then there exists $c>0$ such that Hardy-Littlewood maximal operator is bounded in $L^{p(\\cdot)+c}[0;1].$ Also There exists exponent $p(\\cdot)\\in BMO^{1/\\log},$ ($1<p_{-}\\leq p_{+}<\\infty$) such that Hardy-Littlewood maximal operator is not bounded in $L^{p(\\cdot)}[0;1]$. In the present paper we construct exponent $p(\\cdot),$ $(1<p_{-}\\leq p_{+}<\\infty)$, $1/p(\\cdot)\\in BLO^{1/\\log}$ such that Hardy-Littlewood maximal operator is not bounded in $L^{p(\\cdot)}[0;1]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-21T15:13:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B35"
    ],
    "keywords": [
      "hardy-littlewood maximal operator",
      "construct exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}