{
  "id": "1408.2018",
  "version": "v2",
  "published": "2014-08-09T04:09:59.000Z",
  "updated": "2014-09-04T15:49:14.000Z",
  "title": "New moduli of smoothness",
  "authors": [
    "K. A. Kopotun",
    "D. Leviatan",
    "I. A. Shevchuk"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we discuss various properties of the new modulus of smoothness \\[ \\omega^\\varphi_{k,r}(f^{(r)},t)_p := \\sup_{0 < h\\leq t}\\|\\mathcal W^r_{kh}(\\cdot) \\Delta_{h\\varphi(\\cdot)}^k (f^{(r)},\\cdot)\\|_{L_p[-1,1]}, \\] where $\\mathcal W_\\delta(x) = \\bigl((1-x-\\delta\\varphi(x)/2) (1+x-\\delta\\varphi(x)/2)\\bigr)^{1/2}. $ Related moduli with more general weights are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-09T04:09:59.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-04T15:49:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A17",
      "41A10",
      "42A10",
      "41A25",
      "41A27"
    ],
    "keywords": [
      "smoothness",
      "general weights"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2018K"
    }
  }
}