{
  "id": "2403.04285",
  "version": "v1",
  "published": "2024-03-07T07:34:18.000Z",
  "updated": "2024-03-07T07:34:18.000Z",
  "title": "New Multilinear Littlewood--Paley $g_λ^{*}$ Function and Commutator on weighted Lebesgue Spaces with New Weight",
  "authors": [
    "Huimin Sun",
    "Shuhui Yang",
    "Yan Lin"
  ],
  "comment": "28 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Via the new weight function $A_{\\vec p}^{\\theta }(\\varphi )$, the authors introduce a new class of multilinear Littlewood--Paley $g_{\\lambda}^{*}$ functions and establish the boundedness on weighted Lebesgue spaces. In addition, the authors obtain the boundedness of the multilinear commutator and multilinear iterated commutator generated by the multilinear Littlewood--Paley $g_{\\lambda}^{*}$ function and the new $BMO$ function on weighted Lebesgue spaces. The results in this article include the known results in \\cite{XY2015,SXY2014}. When $m=1$, that is, in the case of one-linear, our conclusions are also new, further extending the results in \\cite{S1961}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-07T07:34:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B35"
    ],
    "keywords": [
      "weighted lebesgue spaces",
      "multilinear littlewood-paley",
      "weight function",
      "boundedness",
      "multilinear iterated commutator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}