{
  "id": "1404.7068",
  "version": "v1",
  "published": "2014-04-28T17:38:14.000Z",
  "updated": "2014-04-28T17:38:14.000Z",
  "title": "Regularization of Newtonian functions via weak boundedness of maximal operators",
  "authors": [
    "Lukáš Malý"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric measure spaces defined via (weak) upper gradients. Our main focus lies on metric spaces with a doubling measure that support a $p$-Poincar\\'e inequality. Absolute continuity of the function lattice quasi-norm is shown to be crucial for approximability by (locally) Lipschitz functions. The proof of the density result uses, among others, that a suitable maximal operator is locally weakly bounded. In particular, various sufficient conditions for such boundedness on rearrangement-invariant spaces are established and applied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-28T17:38:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "30L99",
      "42B25",
      "46E30"
    ],
    "keywords": [
      "maximal operator",
      "weak boundedness",
      "newtonian functions",
      "regularization",
      "lipschitz functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.7068M"
    }
  }
}