{
  "id": "2402.09054",
  "version": "v2",
  "published": "2024-02-14T09:59:00.000Z",
  "updated": "2024-02-15T23:55:57.000Z",
  "title": "The weak (1,1) boundedness of Fourier integral operators with complex phases",
  "authors": [
    "Duván Cardona",
    "Michael Ruzhansky"
  ],
  "comment": "44 Pages; 4 Figures. Theorem 3.1 and Lemma 4.9 have been updated",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "Let $T$ be a Fourier integral operator of order $-(n-1)/2$ associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, Sogge, and Stein proved in the 90's, gives the boundedness of $T$ from the Hardy space $H^1$ into $L^1.$ Additionally, it was shown by T. Tao the weak (1,1) type of $T$. In this work, we establish the weak (1,1) boundedness of a Fourier integral operator $T$ of order $-(n-1)/2$ when it has associated a canonical relation parametrised by a complex phase function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-02-15T23:55:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier integral operator",
      "boundedness",
      "canonical relation",
      "complex phase function",
      "real-phase function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}