{
  "id": "2502.08406",
  "version": "v1",
  "published": "2025-02-12T13:48:35.000Z",
  "updated": "2025-02-12T13:48:35.000Z",
  "title": "Embedding and compact embedding between Bergman and Hardy spaces",
  "authors": [
    "Guanlong Bao",
    "Pan Ma",
    "Fugang Yan",
    "Kehe Zhu"
  ],
  "comment": "21 pages, 1 figure",
  "categories": [
    "math.CV",
    "math.FA"
  ],
  "abstract": "For Hardy spaces and weighted Bergman spaces on the open unit ball in ${\\mathbb C}^n$, we determine exactly when $A^p_\\alpha\\subset H^q$ or $H^p\\subset A^q_\\alpha$, where $0<q<\\infty$, $0<p<\\infty$, and $-\\infty<\\alpha<\\infty$. For each such inclusion we also determine exactly when it is a compact embedding. Although some special cases were known before, we are able to completely cover all possible cases here. We also introduce a new notion called {\\it tight fitting} and formulate a conjecture in terms of it, which places several prominent known results about contractive embeddings in the same framework.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-12T13:48:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hardy spaces",
      "compact embedding",
      "open unit ball",
      "weighted bergman spaces",
      "special cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}