{
  "id": "1705.04939",
  "version": "v1",
  "published": "2017-05-14T09:30:01.000Z",
  "updated": "2017-05-14T09:30:01.000Z",
  "title": "Weighted estimates for the multilinear maximal function on the upper half-spaces",
  "authors": [
    "Wei Chen",
    "Chunxiang Zhu"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "For a general dyadic grid, we give a Calder\\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of $\\mathfrak{M}.$ We obtain a natural extension to the multilinear setting of Muckenhoupt's weak-type characterization. We also partially obtain characterizations of Muckenhoupt's strong-type inequalities with one weight. Assuming the reverse H\\\"{o}lder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hyt\\\"{o}nen-P\\'{e}rez type weighted estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-14T09:30:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B20",
      "42B35"
    ],
    "keywords": [
      "multilinear maximal function",
      "upper half-spaces",
      "weighted estimates",
      "muckenhoupts strong-type inequalities",
      "general dyadic grid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}