{
  "id": "1910.13183",
  "version": "v1",
  "published": "2019-10-29T10:35:05.000Z",
  "updated": "2019-10-29T10:35:05.000Z",
  "title": "Orlicz spaces associated to a quasi-Banach function space. Applications to vector measures and interpolation",
  "authors": [
    "Ricardo del Campo",
    "Antonio Fernández",
    "Fernando Mayoral",
    "Francisco Naranjo"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We characterize the relatively compact subsets of $L^1\\left(\\| m \\| \\right),$ the quasi-Banach function space associated to the semivariation of a given vector measure $m$ showing that the strong connection between compactness, uniform absolute continuity, uniform integrability, almost order boundedness and L-weak compactness that appears in the classic setting of Lebesgue spaces remains almost invariant in this new context of the Choquet integration. Also we present a de la Vall\\'ee-Poussin type theorem in the context of these spaces $L^1\\left(\\|m\\|\\right)$ that allows us to locate each compact subset of $L^1\\left(\\|m\\|\\right)$ as a compact subset of a smaller quasi-Banach Orlicz space $L^\\Phi\\left(\\|m\\|\\right)$ associated to the semivariation of the measure $m.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-29T10:35:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46G10"
    ],
    "keywords": [
      "quasi-banach function space",
      "vector measure",
      "compact subset",
      "smaller quasi-banach orlicz space",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}