{
  "id": "2203.09058",
  "version": "v1",
  "published": "2022-03-17T03:42:00.000Z",
  "updated": "2022-03-17T03:42:00.000Z",
  "title": "On the $L^2$ boundedness of pseudo-multipliers for Hermite expansions",
  "authors": [
    "Fu Ken Ly"
  ],
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this article we develop a new integration by-parts formula for Hermite expansions and use this to give various conditions for Hermite pseudo-multipliers to be bounded on $L^2(\\mathbb{R}^n)$. As a by-product we also give results on $L^p(\\mathbb{R}^n)$, as well as new results for pseudo-multipliers for the Gaussian measure setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-17T03:42:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "33C45",
      "35S05",
      "42B20"
    ],
    "keywords": [
      "hermite expansions",
      "boundedness",
      "integration by-parts formula",
      "hermite pseudo-multipliers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}