{
  "id": "1505.05416",
  "version": "v1",
  "published": "2015-05-20T15:19:47.000Z",
  "updated": "2015-05-20T15:19:47.000Z",
  "title": "Anisotropic Ornstein non inequalities",
  "authors": [
    "Krystian Kazaniecki",
    "Dmitriy M. Stolyarov",
    "Michal Wojciechowski"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We investigate existence of a priori estimates for differential operators in $L^1$ norm: for anisotropic homogeneous differential operators $T_1, \\ldots , T_{\\ell}$, we study the conditions under which the inequality $$ \\|T_1 f\\|_{L_1(\\mathbb{R}^d)} \\lesssim \\sum\\limits_{j = 2}^{\\ell}\\|T_j f\\|_{L_1(\\mathbb{R}^d)} $$ holds true. We also discuss a similar problem for martingale transforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-20T15:19:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inequality",
      "anisotropic ornstein non inequalities",
      "anisotropic homogeneous differential operators",
      "priori estimates",
      "holds true"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150505416K"
    }
  }
}