{
  "id": "2107.09958",
  "version": "v1",
  "published": "2021-07-21T09:10:39.000Z",
  "updated": "2021-07-21T09:10:39.000Z",
  "title": "Hardy spaces on homogeneous trees with flow measures",
  "authors": [
    "Federico Santagati"
  ],
  "comment": "22 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We consider a homogeneous tree endowed with a nondoubling flow measure $\\mu$ of exponential growth and a probabilistic Laplacian $\\mathcal{L}$ self-adjoint with respect to $\\mu$. We prove that the maximal characterization in terms of the heat and the Poisson semigroup of $\\mathcal{L}$ and the Riesz transform characterization of the atomic Hardy space introduced in a previous work fail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-21T09:10:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C21",
      "30H10",
      "35K08",
      "42B25",
      "43A99"
    ],
    "keywords": [
      "homogeneous tree",
      "atomic hardy space",
      "riesz transform characterization",
      "work fail",
      "probabilistic laplacian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}