{
  "id": "2203.08661",
  "version": "v1",
  "published": "2022-03-16T14:51:45.000Z",
  "updated": "2022-03-16T14:51:45.000Z",
  "title": "Another approach to weighted inequalities for a superposition of Copson and Hardy operators",
  "authors": [
    "Rza Mustafayev",
    "Merve Yılmaz"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we present a solution to the inequality $$ \\bigg( \\int_0^{\\infty} \\bigg( \\int_x^{\\infty} \\bigg( \\int_0^t h \\bigg)^q w(t)\\,dt \\bigg)^{r / q} u(x)\\,ds \\bigg)^{1/r}\\leq C \\, \\bigg( \\int_0^{\\infty} h^p v \\bigg)^{1 / p}, \\quad h \\in {\\mathfrak M}^+(0,\\infty), $$ using a combination of reduction techniques and discretization. Here $1 \\le p < \\infty$, $0 < q ,\\, r < \\infty$ and $u,\\,v,\\,w$ are weight functions on $(0,\\infty)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-16T14:51:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "26D15"
    ],
    "keywords": [
      "hardy operators",
      "weighted inequalities",
      "inequality",
      "superposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}