{
  "id": "2203.04720",
  "version": "v1",
  "published": "2022-03-09T13:52:02.000Z",
  "updated": "2022-03-09T13:52:02.000Z",
  "title": "Multi-sublinear operators and their commutators on product generalized mixed Morrey spaces",
  "authors": [
    "Mingquan Wei"
  ],
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "In this paper, we study the boundedness for a large class of multi-sublinear operators $T_m$ generated by multilinear Calder{\\'o}n-Zygmund operators and their commutators $T^{b}_{m,i}~(i=1,\\cdots,m)$ on the product generalized mixed Morrey spaces $M^{\\varphi_1}_{\\vec{q_1}}({\\Bbb R}^n)\\times\\cdots\\times M^{\\varphi_m}_{\\vec{q_m}}({\\Bbb R}^n)$. We find the sufficient conditions on $(\\varphi_1,\\cdots,\\varphi_m,\\varphi)$ which ensure the boundedness of the operator $T_m$ from $M^{\\varphi_1}_{\\vec{q_1}}({\\Bbb R}^n)\\times\\cdots\\times M^{\\varphi_m}_{\\vec{q_m}}({\\Bbb R}^n)$ to $M^{\\varphi}_{\\vec{q}}({\\Bbb R}^n)$. Moreover, the sufficient conditions for the boundeness of $T^b_{m,i}$ from $M^{\\varphi_1}_{\\vec{q_1}}({\\Bbb R}^n)\\times\\cdots\\times M^{\\varphi_m}_{\\vec{q_m}}({\\Bbb R}^n)$ to $M^{\\varphi}_{\\vec{q}}({\\Bbb R}^n)$ are also studied. As applications, we obtain the boundedness for the multi-sublinear maximal operator, the multilinear Calder{\\'o}n-Zygmund operator and their commutators on product generalzied mixed Morrey spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-09T13:52:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B35"
    ],
    "keywords": [
      "product generalized mixed morrey spaces",
      "multi-sublinear operators",
      "commutators",
      "multilinear calder",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}