{
  "id": "2407.01584",
  "version": "v1",
  "published": "2024-06-18T12:21:28.000Z",
  "updated": "2024-06-18T12:21:28.000Z",
  "title": "The mapping properties of fractional derivatives in weighted fractional Sobolev space",
  "authors": [
    "Cailing Li"
  ],
  "categories": [
    "math.CA",
    "math.AP",
    "math.PR"
  ],
  "abstract": "We study the mapping behavior of the Marchaud fractional derivative with different extensions in the scale of fractional weighted Sobolev spaces. In particular we show that the $\\alpha$--order Riemann--Liouville fractional derivative maps $W^{p,s}_0(\\Omega)$ to $W^{p,s-\\alpha}(\\Omega)$, for all $0<\\alpha<s<1$ and the $\\alpha$--order Marchaud fractional derivative with even extension maps the fractional Sobolev space $W^{p,s}((0,\\infty))$ to $W^{p,s-\\alpha}(\\real)$ for all $0<\\alpha<s<1$ and $ps\\geq1$ . The proof is based on the Calder\\'{o}n--Lions interpolation theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-18T12:21:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted fractional sobolev space",
      "mapping properties",
      "order riemann-liouville fractional derivative maps",
      "marchaud fractional derivative",
      "fractional weighted sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}