{
  "id": "1802.01726",
  "version": "v1",
  "published": "2018-02-05T23:15:53.000Z",
  "updated": "2018-02-05T23:15:53.000Z",
  "title": "On embeddings between spaces of functions of generalized bounded variation",
  "authors": [
    "G. H. Esslamzadeh",
    "M. Moazami Goodarzi"
  ],
  "comment": "7 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this note, we aim to establish a number of embeddings between various function spaces that are frequently considered in the theory of Fourier series. More specifically, we give sufficient conditions for the embeddings $\\Phi V[h]\\subseteq \\Lambda\\text{BV}^{(p_n\\uparrow p)}$, $\\Lambda V[h_1]^{(p)}\\subseteq\\Gamma V[h_2]^{(q)}$ and $\\Lambda\\text{BV}^{(p_n\\uparrow p)}\\subseteq\\Gamma\\text{BV}^{(q_n\\uparrow q)}$. Our results are new even for the well-known spaces that have been studied in the literature. In particular, a number of results due to M. Avdispahi\\'{c}, that describe relationships between the classes $\\Lambda\\text{BV}$ and $V[h]$, are derived as special cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-05T23:15:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "26A45"
    ],
    "keywords": [
      "generalized bounded variation",
      "embeddings",
      "fourier series",
      "special cases",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}