{
  "id": "2010.08632",
  "version": "v1",
  "published": "2020-10-16T21:19:51.000Z",
  "updated": "2020-10-16T21:19:51.000Z",
  "title": "Optimality of function spaces for kernel integral operators",
  "authors": [
    "Jakub Takáč"
  ],
  "comment": "27 pages, submitted to Matematische Nachrichten",
  "categories": [
    "math.FA"
  ],
  "abstract": "We explore boundedness properties of kernel integral operators acting on rearrangement-invariant (r.i.) spaces. In particular, for a given r.i. space $X$ we characterize its optimal range partner, that is, the smallest r.i. space $Y$ such that the operator is bounded from $X$ to $Y$. We apply the general results to Lorentz spaces to illustrate their strength.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-16T21:19:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B34",
      "46E30"
    ],
    "keywords": [
      "function spaces",
      "optimality",
      "optimal range partner",
      "boundedness properties",
      "lorentz spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}