{
  "id": "1208.6184",
  "version": "v2",
  "published": "2012-08-30T14:19:10.000Z",
  "updated": "2013-01-27T22:46:07.000Z",
  "title": "On a Local Mean Oscillation Decomposition",
  "authors": [
    "Jonathan Poelhuis",
    "Alberto Torchinsky"
  ],
  "comment": "14 pages. Typos corrected, and Sections 2 and 5 are added. In particular, Section 2 contains a new proof of the pointwise inequality for singular integrals",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this note we generate two local median oscillation decompositions of an arbitrary measurable function and discuss some applications to Calder\\'{o}n-Zygmund singular integral operators $T$. These applications rely on the inequality $M^{\\sharp}_{0,s}(Tf)(x) \\leq c\\,Mf(x)$, and we complete the results given here with a discussion of a local version of this estimate.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-27T22:46:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "46E30"
    ],
    "keywords": [
      "local mean oscillation decomposition",
      "local median oscillation decompositions",
      "singular integral operators",
      "arbitrary measurable function",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.6184P"
    }
  }
}