{
  "id": "2102.07892",
  "version": "v1",
  "published": "2021-02-15T23:15:48.000Z",
  "updated": "2021-02-15T23:15:48.000Z",
  "title": "Covariant Functions of Characters of Compact Subgroups",
  "authors": [
    "Arash Ghaani Farashahi"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper presents a systematic study for abstract harmonic analysis on classical Banach spaces of covariant functions of characters of compact subgroups. Let $G$ be a locally compact group and $H$ be a compact subgroup of $G$. Suppose that $\\xi:H\\to\\mathbb{T}$ is a continuous character, $1\\le p<\\infty$ and $L_\\xi^p(G,H)$ is the set of all covariant functions of $\\xi$ in $L^p(G)$. It is shown that $L^p_\\xi(G,H)$ is isometrically isomorphic to a quotient space of $L^p(G)$. It is also proven that $L^q_\\xi(G,H)$ is isometrically isomorphic to the dual space $L^p_\\xi(G,H)^*$, where $q$ is the conjugate exponent of $p$. The paper is concluded by some results for the case that $G$ is compact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-15T23:15:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A15",
      "43A20",
      "43A85"
    ],
    "keywords": [
      "covariant functions",
      "compact subgroup",
      "abstract harmonic analysis",
      "isometrically isomorphic",
      "quotient space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}