{
  "id": "1803.02177",
  "version": "v1",
  "published": "2018-03-06T13:55:56.000Z",
  "updated": "2018-03-06T13:55:56.000Z",
  "title": "Homeomorphic Changes of Variable and Fourier Multipliers",
  "authors": [
    "V. Lebedev",
    "A. Olevskii"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider the algebras $M_p$ of Fourier multipliers and show that every bounded continuous function $f$ on $\\mathbb R^d$ can be transformed by an appropriate homeomorphic change of variable into a function that belongs to $M_p(\\mathbb R^d)$ for all $p$, $1<p<\\infty$. Moreover, under certain assumptions on a family $K$ of continuous functions, one change of variable will suffice for all $f\\in K$. A similar result holds for functions on the torus $\\mathbb T^d$. This may be contrasted with the known result on the Wiener algebra, related to Luzin's rearrangement problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-06T13:55:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A45",
      "42B15"
    ],
    "keywords": [
      "fourier multipliers",
      "appropriate homeomorphic change",
      "continuous function",
      "similar result holds",
      "luzins rearrangement problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}