{
  "id": "2305.04016",
  "version": "v1",
  "published": "2023-05-06T11:18:17.000Z",
  "updated": "2023-05-06T11:18:17.000Z",
  "title": "A $(φ_\\frac{n}{s}, φ)$-Poincaré inequality in John domain",
  "authors": [
    "Shangying Feng",
    "Tian Liang"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\Omega$ be a bounded domain in $\\mathbb{R}^n$ with $n\\ge2$ and $s\\in(0,1)$. Assume that $\\phi : [0, \\infty) \\to [0, \\infty)$ be a Young function obeying the doubling condition with the constant $K_\\phi<2^{\\frac{n}{s}}$. We demonstrate that $\\Omega $ supports a $(\\phi_\\frac{n}{s}, \\phi)$-Poincar\\'e inequality if it is is a John domain. Alternately, assume further that $\\Omega$ is a bounded domain that is quasiconformally equivalent to some uniform domain when $n\\ge3$ or a simply connected domain when $n=2$. We demonstrate $\\Omega$ is a John domain if a $(\\phi_\\frac{n}{s}, \\phi)$-Poincar\\'e inequality holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-06T11:18:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "john domain",
      "bounded domain",
      "poincare inequality holds",
      "demonstrate",
      "uniform domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}