{
  "id": "1608.07199",
  "version": "v1",
  "published": "2016-08-25T15:35:57.000Z",
  "updated": "2016-08-25T15:35:57.000Z",
  "title": "A Two-weight inequality between $L^p(\\ell^2)$ and $L^p$",
  "authors": [
    "Tuomas Hytönen",
    "Emil Vuorinen"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider boundedness of a certain positive dyadic operator $$ T^\\sigma \\colon L^p(\\sigma; \\ \\! \\ell^2) \\to L^p(\\omega), $$ that arose during our attempts to develop a two-weight theory for the Hilbert transform in $L^p$. Boundedness of $T^\\sigma$ is characterized when $p \\in [2, \\infty)$ in terms of certain testing conditions. This requires a new Carleson-type embedding theorem that is also proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-25T15:35:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "two-weight inequality",
      "boundedness",
      "carleson-type embedding theorem",
      "positive dyadic operator",
      "hilbert transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}