{
  "id": "2403.17943",
  "version": "v1",
  "published": "2024-02-19T10:04:37.000Z",
  "updated": "2024-02-19T10:04:37.000Z",
  "title": "A $(φ_n, φ)$-Poincaré inequality on John domain",
  "authors": [
    "Shangying Feng",
    "Tian Liang"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2305.04016",
  "categories": [
    "math.FA"
  ],
  "abstract": "Given a bounded domain $\\Omega \\subset {\\mathbb R}^{n}$ with $n\\ge2$, let $\\phi $ is a Young function satisfying the doubling condition with the constant $K_\\phi<2^{n}$. If $\\Omega$ is a John domain, we show that $\\Omega $ supports a $(\\phi_{n}, \\phi)$-Poincar\\'e inequality. Conversely, assume additionally that $\\Omega$ is simply connected domain when $n=2$ or a bounded domain which is quasiconformally equivalent to some uniform domain when $n\\ge3$. If $\\Omega$ supports a $(\\phi_n, \\phi)$-Poincar\\'e inequality, we show that it is a John domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-19T10:04:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "john domain",
      "poincare inequality",
      "bounded domain",
      "uniform domain",
      "simply connected domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}