{
  "id": "2310.13567",
  "version": "v1",
  "published": "2023-10-20T15:06:14.000Z",
  "updated": "2023-10-20T15:06:14.000Z",
  "title": "Mapping properties of Fourier transforms, revisited",
  "authors": [
    "Dorothee D. Haroske",
    "Leszek Skrzypczak",
    "Hans Triebel"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished Besov spaces $B^s_p(\\mathbb{R}^n) = B^s_{p,p}(\\mathbb{R}^n)$, $1\\le p \\le \\infty$, and between Sobolev spaces $H^s_p(\\mathbb{R}^n)$, $1<p< \\infty$. In contrast to the paper {\\em H. Triebel, Mapping properties of Fourier transforms. Z. Anal. Anwend. 41 (2022), 133--152}, based mainly on embeddings between related weighted spaces, we rely on wavelet expansions, duality and interpolation of corresponding (unweighted) spaces, and (appropriately extended) Hausdorff-Young inequalities. The degree of compactness will be measured in terms of entropy numbers and approximation numbers, now using the symbiotic relationship to weighted spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-20T15:06:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35"
    ],
    "keywords": [
      "fourier transform",
      "mapping properties",
      "compact mappings",
      "paper deals",
      "sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}