{
  "id": "1711.01484",
  "version": "v1",
  "published": "2017-11-04T19:53:02.000Z",
  "updated": "2017-11-04T19:53:02.000Z",
  "title": "Regularity of maximal functions on Hardy-Sobolev spaces",
  "authors": [
    "Carlos Pérez",
    "Tiago Picon",
    "Olli Saari",
    "Mateus Sousa"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy-Sobolev spaces $\\dot{H}^{1,p}(\\mathbb{R}^d)$ when $1/p < 1+1/d$. This range of exponents is sharp. As a by-product of the proof, we obtain similar results for the local Hardy-Sobolev spaces $\\dot{h}^{1,p}(\\mathbb{R}^d)$ in the same range of exponents.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-04T19:53:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B30",
      "46E35"
    ],
    "keywords": [
      "maximal functions",
      "regularity",
      "local hardy-sobolev spaces",
      "convolution type",
      "smooth kernels"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}