{
  "id": "2308.06048",
  "version": "v1",
  "published": "2023-08-11T09:52:22.000Z",
  "updated": "2023-08-11T09:52:22.000Z",
  "title": "Hölder continuity of functions in the fractional Sobolev spaces: 1-dimensional case",
  "authors": [
    "Yan Rybalko"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with the embedding of the Sobolev spaces of fractional order into the space of H\\\"older continuous functions. More precisely, we show that the function $f\\in H^s(\\mathbb{R})$ with $\\frac{1}{2}<s<1$ is H\\\"older continuous with the exponent $s-\\frac{1}{2}$. Our result is an improvement of the Sobolev embedding theorem in the one dimensional case, which states that every such a function $f$ is continuous. The H\\\"older exponent $s-\\frac{1}{2}$ is consistent with the Morrey's inequality, which yields that $f\\in H^1(\\mathbb{R})$ is H\\\"older continuous with the exponent $\\frac{1}{2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-11T09:52:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional sobolev spaces",
      "hölder continuity",
      "morreys inequality",
      "paper deals",
      "continuous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}