{
  "id": "2410.20719",
  "version": "v1",
  "published": "2024-10-28T04:31:54.000Z",
  "updated": "2024-10-28T04:31:54.000Z",
  "title": "Uniform boundary Harnack principle for non-local operators on metric measure spaces",
  "authors": [
    "Shiping Cao",
    "Zhen-Qing Chen"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain a uniform boundary Harnack principle (BHP) on any open sets for a large class of non-local operators on metric measure spaces under a jump measure comparability and tail estimate condition, and an upper bound condition on the distribution function for the exit times from balls. These conditions are satisfied by any non-local operator $\\mathcal{L}$ that admits a two-sided mixed stable-like heat kernel bounds when the underlying metric measure spaces have volume doubling and reverse volume doubling properties. The results of this paper are new even for non-local operators on Euclidean spaces. In particular, our results give not only the scale invariant but also uniform BHP for the first time for non-local operators on Euclidean spaces of both divergence form and non-divergence form with measurable coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-28T04:31:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniform boundary harnack principle",
      "metric measure spaces",
      "non-local operator",
      "stable-like heat kernel bounds",
      "mixed stable-like heat kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}