{
  "id": "2310.01817",
  "version": "v1",
  "published": "2023-10-03T06:15:25.000Z",
  "updated": "2023-10-03T06:15:25.000Z",
  "title": "The Note on the Closure of Continuous Functions in Variable-Exponent Lebesgue Spaces for Multiple Variables",
  "authors": [
    "Nikoloz Devdariani"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we generalize a recently obtained result by Kopaliani and Zviadadze from the one-variable case to the several-variable case. Specifically, in terms of decreasing rearrangement, we characterize those exponents $p(\\cdot)$ for which the corresponding variable-exponent Lebesgue space $L^{p(\\cdot)}([0;1]^n)$ shares the property with $L^\\infty([0;1]^n)$ such that the space of continuous functions $C([0;1]^n)$ forms a closed linear subspace in $L^{p(\\cdot)}([0;1]^n)$ . In particular, we derive the necessary and sufficient conditions on the decreasing rearrangement of the exponent $p(\\cdot)$ for which there exists an equimeasurable exponent of $p(\\cdot)$ such that the corresponding variable-exponent Lebesgue space possesses the aforementioned property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-03T06:15:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46E15"
    ],
    "keywords": [
      "continuous functions",
      "multiple variables",
      "corresponding variable-exponent lebesgue space possesses",
      "decreasing rearrangement",
      "linear subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}