{
  "id": "2002.11520",
  "version": "v1",
  "published": "2020-02-25T16:11:28.000Z",
  "updated": "2020-02-25T16:11:28.000Z",
  "title": "Self-improvement of weighted pointwise inequalities on open sets",
  "authors": [
    "Sylvester Eriksson-Bique",
    "Juha Lehrbäck",
    "Antti V. Vähäkangas"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1810.07614",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincar\\'e and $p$-Hardy weights for an open set $\\Omega\\subset X$, where $X$ is a metric measure space. We also apply the self-improvement of weighted pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-25T16:11:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A23",
      "42B25",
      "31E05"
    ],
    "keywords": [
      "weighted pointwise inequalities",
      "open set",
      "general self-improvement property",
      "metric measure space",
      "usual integral versions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}