{
  "id": "1907.12788",
  "version": "v1",
  "published": "2019-07-30T09:05:23.000Z",
  "updated": "2019-07-30T09:05:23.000Z",
  "title": "Properties of moduli of smoothness in $L_p(\\mathbb{R}^d)$",
  "authors": [
    "Yurii Kolomoitsev",
    "Sergey Tikhonov"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we discuss various basic properties of moduli of smoothness of functions from $L_p(\\mathbb{R}^d)$, $0<p\\le \\infty$. In particular, complete versions of Jackson-, Marchaud-, and Ulyanov-type inequalities are given for the whole range of $p$. Moreover, equivalences between moduli of smoothness and the corresponding $K$-functionals and the realization concept are proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-30T09:05:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A17",
      "41A63",
      "26D10",
      "26D15",
      "41A25",
      "46E35",
      "26A33"
    ],
    "keywords": [
      "smoothness",
      "basic properties",
      "complete versions",
      "ulyanov-type inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}