{
  "id": "math/0609535",
  "version": "v1",
  "published": "2006-09-19T20:29:34.000Z",
  "updated": "2006-09-19T20:29:34.000Z",
  "title": "Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type",
  "authors": [
    "A. Brudnyi",
    "Yu. Brudnyi"
  ],
  "comment": "12 pages",
  "journal": "Rev. Mat. Complut., 19 (2006), no. 2, 347-359",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "If a metric subspace $M^{o}$ of an arbitrary metric space $M$ carries a doubling measure $\\mu$, then there is a simultaneous linear extension of all Lipschitz functions on $M^{o}$ ranged in a Banach space to those on $M$. Moreover, the norm of this linear operator is controlled by logarithm of the doubling constant of $\\mu$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-19T20:29:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B35",
      "54E35",
      "46B15"
    ],
    "keywords": [
      "lipschitz functions",
      "metric subspace",
      "homogeneous type",
      "arbitrary metric space",
      "linear operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9535B"
    }
  }
}