{
  "id": "1507.07866",
  "version": "v1",
  "published": "2015-07-28T17:38:59.000Z",
  "updated": "2015-07-28T17:38:59.000Z",
  "title": "Embeddings between weighted Copson and Cesàro function spaces",
  "authors": [
    "Amiran Gogatishvili",
    "Rza Mustafayev",
    "Tuǧçe Ünver"
  ],
  "comment": "25 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper embeddings between weighted Copson function spaces ${\\operatorname{Cop}}_{p_1,q_1}(u_1,v_1)$ and weighted Ces\\`{a}ro function spaces ${\\operatorname{Ces}}_{p_2,q_2}(u_2,v_2)$ are characterized. In particular, two-sided estimates of the optimal constant $c$ in the inequality \\begin{equation*} \\bigg( \\int_0^{\\infty} \\bigg( \\int_0^t f(\\tau)^{p_2}v_2(\\tau)\\,d\\tau\\bigg)^{\\frac{q_2}{p_2}} u_2(t)\\,dt\\bigg)^{\\frac{1}{q_2}} \\le c \\bigg( \\int_0^{\\infty} \\bigg( \\int_t^{\\infty} f(\\tau)^{p_1} v_1(\\tau)\\,d\\tau\\bigg)^{\\frac{q_1}{p_1}} u_1(t)\\,dt\\bigg)^{\\frac{1}{q_1}}, \\end{equation*} where $p_1,\\,p_2,\\,q_1,\\,q_2 \\in (0,\\infty)$, $p_2 \\le q_2$ and $u_1,\\,u_2,\\,v_1,\\,v_2$ are weights on $(0,\\infty)$, are obtained. The most innovative part consists of the fact that possibly different parameters $p_1$ and $p_2$ and possibly different inner weights $v_1$ and $v_2$ are allowed. The proof is based on the combination duality techniques with estimates of optimal constants of the embeddings between weighted Ces\\`{a}ro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of the iterated Hardy-type inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-28T17:38:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "26D10"
    ],
    "keywords": [
      "cesàro function spaces",
      "optimal constant",
      "weighted copson function spaces",
      "combination duality techniques",
      "iterated hardy-type inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150707866G"
    }
  }
}