{
  "id": "2001.07200",
  "version": "v1",
  "published": "2020-01-20T18:18:52.000Z",
  "updated": "2020-01-20T18:18:52.000Z",
  "title": "Dyadic decomposition of convex domains of finite type and applications",
  "authors": [
    "Chun Gan",
    "Bingyang Hu",
    "Ilyas Khan"
  ],
  "comment": "24 pages, 4 figures",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called dyadic flow tents. This dyadic structure allows us to establish weighted norm estimates for the Bergman projection $P$ on such domains with respect to Muckenhoupt weights. In particular, this result gives an alternative proof of the $L^p$ boundedness of $P$. Moreover, using extrapolation, we are also able to derive weighted vector-valued estimates and weighted modular inequalities for the Bergman projection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-20T18:18:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32A36",
      "42B35"
    ],
    "keywords": [
      "convex domains",
      "finite type",
      "dyadic decomposition",
      "dyadic structure",
      "bergman projection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}