{
  "id": "1207.5551",
  "version": "v2",
  "published": "2012-07-23T22:30:54.000Z",
  "updated": "2012-11-15T19:57:40.000Z",
  "title": "One and two weight norm inequalities for Riesz potentials",
  "authors": [
    "David Cruz-Uribe",
    "Kabe Moen"
  ],
  "comment": "v2 typos corrected. Illinois J. Math. to appear",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider weighted norm inequalities for the Riesz potentials $I_\\alpha$, also referred to as fractional integral operators. First we prove mixed $A_p$-$A_\\infty$ type estimates in the spirit of [13, 15, 17]. Then we prove strong and weak type inequalities in the case $p<q$ using the so-called log bump conditions. These results complement the strong type inequalities of P\\'erez [30] and answer a conjecture from [3]. For both sets of results our main tool is a corona decomposition adapted to fractional averages.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-15T19:57:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weight norm inequalities",
      "riesz potentials",
      "log bump conditions",
      "fractional integral operators",
      "weak type inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.5551C"
    }
  }
}