{
  "id": "1105.6152",
  "version": "v1",
  "published": "2011-05-31T02:53:23.000Z",
  "updated": "2011-05-31T02:53:23.000Z",
  "title": "On the Good-$λ$ inequality for nonlinear potentials",
  "authors": [
    "Petr Honzík",
    "Benjamin J. Jaye"
  ],
  "comment": "13 pages, submitted",
  "journal": "Proc. Amer. Math. Soc. 140 (2012), no. 12, 4167--4180",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "This note concerns an extension of the good-$\\lambda$ inequality for fractional integrals, due to B. Muckenhoupt and R. Wheeden. The classical result is refined in two aspects. Firstly, general nonlinear potentials are considered; and secondly, the constant in the inequality is proven to decay exponentially. As a consequence, the exponential integrability of the gradient of solutions to certain quasilinear elliptic equations is deduced. This in turn is a consequence of certain Morrey space embeddings which extend classical results for the Riesz potential. In addition, the good-$\\lambda$ inequality proved here provides an elementary proof of the result of Jawerth, Perez and Welland regarding the positive cone in certain weighted Triebel-Lizorkin spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-31T02:53:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inequality",
      "morrey space embeddings",
      "quasilinear elliptic equations",
      "general nonlinear potentials",
      "consequence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.6152H"
    }
  }
}