{
  "id": "2008.04494",
  "version": "v1",
  "published": "2020-08-11T03:12:23.000Z",
  "updated": "2020-08-11T03:12:23.000Z",
  "title": "Cwikel-Solomyak estimates on tori and Euclidean spaces",
  "authors": [
    "Fedor Sukochev",
    "Dmitriy Zanin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We revise Cwikel-type estimate for the singular values of the operator $(1-\\Delta_{\\mathbb{T}^d})^{-\\frac{d}{4}}M_f(1-\\Delta_{\\mathbb{T}^d})^{-\\frac{d}{4}}$ on the torus $\\mathbb{T}^d$ for the ideal $\\mathcal{L}_{1,\\infty}$, established by M.Z. Solomyak in even dimensions in \\cite{Solomyak1995}, and extend it to odd dimensions. We obtain a new result for (symmetrized) Cwikel type estimates for Laplacians on $\\mathbb{R}^d$ for arbitrary positive integer $d.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-11T03:12:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euclidean spaces",
      "cwikel-solomyak estimates",
      "revise cwikel-type estimate",
      "cwikel type estimates",
      "odd dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}