{
  "id": "2410.22301",
  "version": "v1",
  "published": "2024-10-29T17:48:33.000Z",
  "updated": "2024-10-29T17:48:33.000Z",
  "title": "On weighted Cesàro function spaces",
  "authors": [
    "Amiran Gogatishvili",
    "Tuğçe Ünver"
  ],
  "categories": [
    "math.FA",
    "math.AP",
    "math.CA"
  ],
  "abstract": "The main objective of this paper is to provide a comprehensive demonstration of recent results regarding the structures of the weighted Ces\\`aro and Copson function spaces. These spaces' definitions involve local and global weighted Lebesgue norms; in other words, the norms of these spaces are generated by positive sublinear operators and by weighted Lebesgue norms. The weighted Lebesgue spaces are the special cases of these spaces with a specific set of parameters. Our primary method of investigating these spaces will be the so-called discretization technique. Our technique will be the development of the approach initiated by K.G. Grosse-Erdmann, which allows us to obtain the characterization in previously unavailable situations, thereby addressing decades-old open problems. We investigate the relation (embeddings) between weighted Ces\\`aro and Copson function spaces. The characterization of these embeddings can be used to tackle the problems of characterizing pointwise multipliers between weighted Ces\\`aro and Copson function spaces, the characterizations of the associate spaces of Ces\\`aro (Copson) function spaces, as well as the relations between local Morrey-type spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-29T17:48:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "46E20"
    ],
    "keywords": [
      "weighted cesàro function spaces",
      "copson function spaces",
      "global weighted lebesgue norms",
      "addressing decades-old open problems",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}