{
  "id": "2311.13316",
  "version": "v1",
  "published": "2023-11-22T11:10:36.000Z",
  "updated": "2023-11-22T11:10:36.000Z",
  "title": "Hardy spaces adapted to elliptic operators on open sets",
  "authors": [
    "Sebastian Bechtel",
    "Tim Böhnlein"
  ],
  "comment": "40 pages",
  "categories": [
    "math.FA",
    "math.AP",
    "math.CA"
  ],
  "abstract": "Let $L= - \\mathrm{div} (A \\nabla \\cdot)$ be an elliptic operator defined on an open subset of $\\mathbb{R}^d$, complemented with mixed boundary conditions. Under suitable assumptions on the operator and the geometry, we derive an atomic characterization (depending only on the boundary conditions) for the Hardy space $H^1_L$ defined using an adapted square function for $L$. This generalizes known results of Auscher and Russ in the case of pure Dirichlet/Neumann boundary conditions on Lipschitz domains. In particular, we develop a connection between the harmonic analysis of $L$ and its underlying geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-22T11:10:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic operator",
      "hardy space",
      "open sets",
      "pure dirichlet/neumann boundary conditions",
      "mixed boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}