{
  "id": "2302.12701",
  "version": "v1",
  "published": "2023-02-24T16:00:03.000Z",
  "updated": "2023-02-24T16:00:03.000Z",
  "title": "Function spaces for decoupling",
  "authors": [
    "Andrew Hassell",
    "Pierre Portal",
    "Jan Rozendaal",
    "Po-Lam Yung"
  ],
  "comment": "41 pages",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We introduce new function spaces $\\mathcal{H}^{p,q;s}_{\\mathrm{dec}}(\\mathbb{R}^{n})$ that yield a natural reformulation of the $\\ell^{q}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half-wave propagators, but not under all Fourier integral operators unless $p=q$, in which case they coincide with the Hardy spaces for Fourier integral operators. We use these spaces to obtain improvements of the classical fractional integration theorem, and local smoothing estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-24T16:00:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42B37",
      "35L05",
      "35S30"
    ],
    "keywords": [
      "function spaces",
      "euclidean half-wave propagators",
      "decoupling",
      "classical fractional integration theorem",
      "fourier integral operators unless"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}