{
  "id": "1708.07343",
  "version": "v1",
  "published": "2017-08-24T10:19:55.000Z",
  "updated": "2017-08-24T10:19:55.000Z",
  "title": "Weak type estimates for functions of Marcinkiewicz type with fractional integrals of mixed homogeneity",
  "authors": [
    "Shuichi Sato"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove the endpoint weak type estimate for square functions of Marcinkiewicz type with fractional integrals associated with non-isotropic dilations. This generalizes a result of C. Fefferman on functions of Marcinkiewicz type by considering fractional integrals of mixed homogeneity in place of the Riesz potentials of Euclidean structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-24T10:19:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E35"
    ],
    "keywords": [
      "marcinkiewicz type",
      "mixed homogeneity",
      "endpoint weak type estimate",
      "square functions",
      "non-isotropic dilations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}