{
  "id": "2410.09966",
  "version": "v1",
  "published": "2024-10-13T19:06:00.000Z",
  "updated": "2024-10-13T19:06:00.000Z",
  "title": "$L^p$-to-$L^q$ boundedness for commutators of the Cauchy transform",
  "authors": [
    "Adam Mair"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we prove a characterization of the $L^p$-to-$L^q$ boundedness of commutators to the Cauchy transform. Our work presents both new results and new proofs for established results. In particular, we show that the Campanato space characterizes boundedness of commutators for a certain range of $p$ and $q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-13T19:06:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25"
    ],
    "keywords": [
      "cauchy transform",
      "commutators",
      "campanato space characterizes boundedness",
      "characterization",
      "established results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}