{
  "id": "2312.02455",
  "version": "v1",
  "published": "2023-12-05T03:12:30.000Z",
  "updated": "2023-12-05T03:12:30.000Z",
  "title": "Boundary Harnack principle for non-local operators on metric measure spaces",
  "authors": [
    "Zhen-Qing Chen",
    "Jie-Ming Wang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, a necessary and sufficient condition is obtained for the scale invariant boundary Harnack inequality (BHP in abbreviation) for a large class of Hunt processes on metric measure spaces that are in weak duality with another Hunt process. We next consider a discontinuous subordinate Brownian motion with Gaussian component $X_t=W_{S_t}$ in ${\\bf R}^d$ for which the L\\'evy density of the subordinator $S$ satisfies some mild comparability condition. We show that the scale invariant BHP holds for the subordinate Brownian motion $X$ in any Lipschitz domain satisfying the interior cone condition with common angle $\\theta\\in (\\cos^{-1}(1/\\sqrt d), \\pi)$, but fails in any truncated circular cone with angle $\\theta \\leq \\cos^{-1}(1/\\sqrt d)$, a Lipschitz domain whose Lipschitz constant is larger than or equal to $1/\\sqrt{d-1}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-05T03:12:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B25",
      "47G20",
      "60J45",
      "60J76"
    ],
    "keywords": [
      "metric measure spaces",
      "boundary harnack principle",
      "non-local operators",
      "subordinate brownian motion",
      "scale invariant boundary harnack inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}