{
  "id": "2305.13708",
  "version": "v1",
  "published": "2023-05-23T05:46:58.000Z",
  "updated": "2023-05-23T05:46:58.000Z",
  "title": "Sobolev type inequalities for fractional maximal functions and Riesz potentials in half spaces",
  "authors": [
    "Yoshihiro Mizuta",
    "Tetsu Shimomura"
  ],
  "comment": "22 pages, to appear in Studia Math",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we study Sobolev type inequalities for fractional maximal functions $M_{{\\mathbb H},\\nu}f$ and Riesz potentials $I_{{\\mathbb H},\\alpha} f$ of functions in weighted Morrey spaces of the double phase functional $\\Phi(x,t) = t^{p} + (b(x) t)^{q}$ in the half space, where $1<p<q$ and $b(\\cdot)$ is non-negative, bounded and H\\\"older continuous of order $\\theta \\in (0,1]$. We also show that the Riesz potential operator $I_{{\\mathbb H},\\alpha}$ embeds from weighted Morrey space of the double phase functional $\\Phi(x,t)$ to weighted Campanato spaces. Finally, we treat the similar embedding for Sobolev functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-23T05:46:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "42B25",
      "31B15"
    ],
    "keywords": [
      "fractional maximal functions",
      "riesz potential",
      "half space",
      "weighted morrey space",
      "double phase functional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}