{
  "id": "2406.10668",
  "version": "v1",
  "published": "2024-06-15T15:27:23.000Z",
  "updated": "2024-06-15T15:27:23.000Z",
  "title": "On boundedness of Hausdorff-type operators on Sobolev spaces",
  "authors": [
    "A. R. Mirotin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A new notion of a Hausdorff-type operator on function spaces over domains in Euclidean spaces is introduced, and a sufficient condition for the boundedness of this operator on Sobolev spaces is proved. It is shown that this condition cannot be weakened in general.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-15T15:27:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A05",
      "44A30",
      "42B35",
      "47G10"
    ],
    "keywords": [
      "sobolev spaces",
      "hausdorff-type operator",
      "boundedness",
      "function spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}