{
  "id": "2410.10001",
  "version": "v1",
  "published": "2024-10-13T20:47:19.000Z",
  "updated": "2024-10-13T20:47:19.000Z",
  "title": "Hardy inequalities and nonlocal capacity",
  "authors": [
    "Tomasz Grzywny",
    "Julia Lenczewska"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this article, we introduce and study capacities related to nonlocal Sobolev spaces, with focus on spaces corresponding to zero-order nonlocal operators. In particular, we prove Hardy-type inequalities to obtain Sobolev embeddings and use them to estimate the nonlocal capacities of a ball.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-13T20:47:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "31B15",
      "46E35"
    ],
    "keywords": [
      "nonlocal capacity",
      "hardy inequalities",
      "nonlocal sobolev spaces",
      "zero-order nonlocal operators",
      "study capacities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}