{
  "id": "2206.02708",
  "version": "v1",
  "published": "2022-06-06T16:06:37.000Z",
  "updated": "2022-06-06T16:06:37.000Z",
  "title": "Modular convergence in $H$-Orlicz spaces of Banach valued functions",
  "authors": [
    "Hemanta Kalita",
    "Bipan Hazarika"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article we develop the theory of $H$-Orlicz space generated by generalised Young function. Modular convergence of $H$-Orlicz space for the case of vector-valued functions and norm convergence in $\\mcH^\\theta(X, \\bar{\\mu})$ where $X$ is any Banach space are discussed. Relationships of modular convergence and norm convergence of $H$-Orlicz spaces are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-06T16:06:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orlicz space",
      "modular convergence",
      "banach valued functions",
      "norm convergence",
      "generalised young function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}