{
  "id": "1708.08606",
  "version": "v1",
  "published": "2017-08-29T06:55:41.000Z",
  "updated": "2017-08-29T06:55:41.000Z",
  "title": "Estimates of Dirichlet heat kernels for subordinate Brownian motions",
  "authors": [
    "Panki Kim",
    "Ante Mimica"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we discuss estimates of transition densities of subordinate Brownian motions in open subsets of Euclidean space. When $D$ is a $C^{1,1}$ domain, we establish sharp two-sided estimates for the transition densities of a large class of subordinate Brownian motions in $D$ whose scaling order is not necessarily strictly below $2$. Our estimates are explicit and written in terms of the dimension, the Euclidean distance between two points, the distance to the boundary and Laplace exponent of the corresponding subordinator only.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-29T06:55:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J35",
      "60J50",
      "60J75"
    ],
    "keywords": [
      "subordinate brownian motions",
      "dirichlet heat kernels",
      "transition densities",
      "open subsets",
      "euclidean space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}