{
  "id": "2208.07215",
  "version": "v1",
  "published": "2022-08-15T14:20:01.000Z",
  "updated": "2022-08-15T14:20:01.000Z",
  "title": "The structure of subspaces in Orlicz spaces between $L^1$ and $L^2$",
  "authors": [
    "S. V. Astashkin"
  ],
  "comment": "24 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "A subspace $H$ of a rearrangement invariant space $X$ on $[0,1]$ is strongly embedded in $X$ if, in $H$, convergence in $X$-norm is equivalent to convergence in measure. We obtain necessary and sufficient conditions on an Orlicz function $M$, under which the unit ball of an arbitrary strongly embedded subspace in the Orlicz space $L_M$ has equi-absolutely continuous norms in $L_M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-15T14:20:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46B03",
      "46B09",
      "46A45"
    ],
    "keywords": [
      "orlicz space",
      "rearrangement invariant space",
      "convergence",
      "sufficient conditions",
      "orlicz function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}