{
  "id": "1505.00518",
  "version": "v1",
  "published": "2015-05-04T03:23:37.000Z",
  "updated": "2015-05-04T03:23:37.000Z",
  "title": "$\\mathbf A_1$-regularity and boundedness of Calderón-Zygmund operators. II",
  "authors": [
    "Dmitry V. Rutsky"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A proof is given for the \"only if\" part of the result stated in the previous article of the series that a suitably nondegenerate Calder\\'on-Zygmund operator $T$ is bounded in a Banach lattice $X$ on $\\mathbb R^n$ if and only if the Hardy-Littlewood maximal operator $M$ is bounded in both $X$ and $X'$, under the assumption that $X$ has the Fatou property and $X$ is $p$-convex and $q$-concave with some $1 < p, q < \\infty$. We also get rid of a fixed point theorem in the proof of the main lemma and give an improved version of an earlier result concerning the divisibility of $\\mathrm {BMO}$-regularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-04T03:23:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B42",
      "42B25",
      "42B20",
      "46E30",
      "47B38"
    ],
    "keywords": [
      "calderón-zygmund operators",
      "regularity",
      "boundedness",
      "hardy-littlewood maximal operator",
      "suitably nondegenerate calderon-zygmund operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}