{
  "id": "2308.13747",
  "version": "v1",
  "published": "2023-08-26T03:13:16.000Z",
  "updated": "2023-08-26T03:13:16.000Z",
  "title": "Extensions and Approximations",
  "authors": [
    "Ikemefuna Agbanusi"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We investigate the order of approximation when certain singular kernels when act on the zero-extension of functions. The results can be repurposed to give non trivial estimates on the moduli of continuity of zero-extensions. Our approach avoids the use of Hardy type inequalities and so applies to any function in $L^p([0,1]^d)$ regardless of smoothness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-26T03:13:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "46E35"
    ],
    "keywords": [
      "approximation",
      "extensions",
      "non trivial estimates",
      "hardy type inequalities",
      "singular kernels"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}