{
  "id": "2201.09328",
  "version": "v1",
  "published": "2022-01-23T17:44:37.000Z",
  "updated": "2022-01-23T17:44:37.000Z",
  "title": "Hausdorff Operators on Compact Abelian Groups",
  "authors": [
    "A. R. Mirotin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces $H^p_E(G)$, real Hardy space $H^1_{\\mathbb{R}}(G)$, $BMO(G)$, and $BMOA(G)$ for compact Abelian group $G$. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continuous functions on $G$ and examples are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-23T17:44:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B90"
    ],
    "keywords": [
      "compact abelian group",
      "hausdorff operators",
      "real hardy space",
      "generalized hardy spaces",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}