{
  "id": "2501.05895",
  "version": "v1",
  "published": "2025-01-10T11:47:22.000Z",
  "updated": "2025-01-10T11:47:22.000Z",
  "title": "Orlicz Space on Groupoids",
  "authors": [
    "K. N. Sridharan",
    "N. Shravan Kumar"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $G$ be a locally compact second countable groupoid with a fixed Haar system $\\lambda=\\{\\lambda^{u}\\}_{u\\in G^{0}}$ and $(\\Phi,\\Psi)$ be a complementary pair of $N$-functions satisfying $\\Delta_{2}$-condition. In this article, we introduce the continuous field of Orlicz space $(L^{\\Phi}_{0},\\Delta_{1})$ and provide a sufficient condition for the space of continuous sections vanishing at infinity, denoted $E^{\\Phi}_{0}$, to be an algebra under a suitable convolution. The condition for a closed $C_{b}(G^{0})$-submodule $I$ of $E^{\\Phi}_{0}$ to be a left ideal is established. Further, we provide a groupoid analogue of the characterization of the space of convolutors of Morse-Transue space for locally compact groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-10T11:47:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18B40",
      "46E30",
      "46H99"
    ],
    "keywords": [
      "orlicz space",
      "locally compact second countable groupoid",
      "complementary pair",
      "sufficient condition",
      "fixed haar system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}