{
  "id": "1312.1991",
  "version": "v3",
  "published": "2013-12-06T20:27:05.000Z",
  "updated": "2014-12-08T16:35:20.000Z",
  "title": "A Hardy inequality and applications to reverse Holder inequalities for weights on $R$",
  "authors": [
    "Eleftherios N. Nikolidakis"
  ],
  "comment": "11 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove a sharp integral inequality valid for non-negative functions defined on $[0,1]$, with given $L^1$ norm. This is in fact a generalization of the well known integral Hardy inequality. We prove it as a consequence of the respective weighted discrete analogue inequality which proof is presented in this paper. As an application we find the exact best possible range of $p>q$ such that any non-increasing $f$ which satisfies a reverse H\\\"{o}lder inequality with exponent $q$ and constant $c$ upon the subintervals of $[0,1]$, should additionally satisfy a reverse H\\\"{o}lder inequality with exponent $p$ and a different in general constant $c'$. The result has been treated in \\cite{1} but here we give an alternative proof based on the above mentioned inequality.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-03T14:39:23.000Z",
      "abstract": "We prove a sharp integral inequality valid for non-negative functions defined on $[0,1]$. This is in fact a generalization of the well known integral Hardy inequality. We prove it as a consequence of the respective weighted discrete analogue inequality which proof is presented in this paper. As an application we find the exact best possible range of $p>q$ such that any non-increasing $f$ which satisfies a reverse H\\\"{o}lder inequality with exponent $q$ and constant $c$ upon the subintervals of $[0,1]$, should additionally satisfy a reverse H\\\"{o}lder inequality with exponent $p$ and a different in general constant $c'$. The result has been treated in \\cite{1} but here we give an alternative proof based on the above mentioned inequality.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-12-08T16:35:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reverse holder inequalities",
      "application",
      "sharp integral inequality valid",
      "integral hardy inequality",
      "respective weighted discrete analogue inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1991N"
    }
  }
}