{
  "id": "2208.09192",
  "version": "v1",
  "published": "2022-08-19T07:33:11.000Z",
  "updated": "2022-08-19T07:33:11.000Z",
  "title": "Potential theory of Dirichlet forms with jump kernels blowing up at the boundary",
  "authors": [
    "Panki Kim",
    "Renming Song",
    "Zoran Vondraček"
  ],
  "comment": "63 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "In this paper we study the potential theory of Dirichlet forms on the half-space $\\mathbb{R}^d_+$ defined by the jump kernel $J(x,y)=|x-y|^{-d-\\alpha}\\mathcal{B}(x,y)$ and the killing potential $\\kappa x_d^{-\\alpha}$, where $\\alpha\\in (0, 2)$ and $\\mathcal{B}(x,y)$ can blow up to infinity at the boundary. The jump kernel and the killing potential depend on several parameters. For all admissible values of the parameters involved and all $d \\ge 1$, we prove that the boundary Harnack principle holds, and establish sharp two-sided estimates on the Green functions of these processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-19T07:33:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J45"
    ],
    "keywords": [
      "dirichlet forms",
      "jump kernels blowing",
      "potential theory",
      "boundary harnack principle holds",
      "killing potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}