{
  "id": "2208.07920",
  "version": "v1",
  "published": "2022-08-16T19:37:59.000Z",
  "updated": "2022-08-16T19:37:59.000Z",
  "title": "Reinforcing a Philosophy: Littlewood-Paley theory for the moment curve",
  "authors": [
    "Kevin Hughes"
  ],
  "comment": "8 pages, related to arXiv:1906.05877, arXiv:2201.09649 and arXiv:2203.13644, comments welcome :)",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "Using the Girard-Newton formulae, I give a simple proof of isotropic square function estimates for extension operators along the moment curve in generic local fields. Using Bezout's Theorem and the Implicit Function Theorem, I give an alternate, sharper proof for real or complex non-degenerate, polynomial curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-16T19:37:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "11D45",
      "11D88"
    ],
    "keywords": [
      "moment curve",
      "littlewood-paley theory",
      "isotropic square function estimates",
      "philosophy",
      "generic local fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}