{
  "id": "2101.07366",
  "version": "v1",
  "published": "2021-01-18T23:09:05.000Z",
  "updated": "2021-01-18T23:09:05.000Z",
  "title": "Convolution Properties of Orlicz Spaces on hypergroups",
  "authors": [
    "A. R. Bagheri Salec",
    "Vishvesh Kumar",
    "S. M. Tabatabaie"
  ],
  "comment": "12 pages. Comments and suggestions are welcome",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, for a locally compact commutative hypergroup $K$ and for a pair $(\\Phi_1, \\Phi_2)$ of Young functions satisfying sequence condition, we give a necessary condition in terms of aperiodic elements of the center of $K,$ for the convolution $f\\ast g$ to exist a.e., where $f$ and $g$ are arbitrary elements of Orlicz spaces $L^{\\Phi_1}(K)$ and $L^{\\Phi_2}(K)$, respectively. As an application, we present some equivalent conditions for compactness of a compactly generated locally compact abelian group. Moreover, we also characterize compact convolution operators from $L^1_w(K)$ into $L^\\Phi_w(K)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-18T23:09:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "43A62",
      "43A15"
    ],
    "keywords": [
      "orlicz spaces",
      "convolution properties",
      "hypergroup",
      "young functions satisfying sequence condition",
      "generated locally compact abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}