{
  "id": "2303.13985",
  "version": "v1",
  "published": "2023-03-24T13:13:20.000Z",
  "updated": "2023-03-24T13:13:20.000Z",
  "title": "$L^p$-boundedness of wave operators for $Δ^2 + V$ on ${\\mathbb R}^4$",
  "authors": [
    "Artbazar Galtbayar",
    "Kenji Yajima"
  ],
  "comment": "77 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that the wave operators of scattering theory for the fourth order Schr\\\"odinger operators $\\Delta^2 + V(x)$ in ${\\mathbb R}^4$ are bounded in $L^p({\\mathbb R}^4)$ for the set of $p$'s of $(1,\\infty)$ depending on the kind of spectral singularities of $H$ at zero which can be described by the space of bounded solutions of $(\\Delta^2 + V(x))u(x)=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-24T13:13:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wave operators",
      "boundedness",
      "fourth order",
      "spectral singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 77,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}