{
  "id": "math/0605533",
  "version": "v3",
  "published": "2006-05-18T21:16:50.000Z",
  "updated": "2006-09-19T04:11:56.000Z",
  "title": "Potential Theory of Truncated Stable Processes",
  "authors": [
    "Panki Kim",
    "Renming Song"
  ],
  "comment": "35 page, to appear in Mathematische Zeitschrift",
  "categories": [
    "math.PR"
  ],
  "abstract": "For any 0 < alpha <2, a truncated symmetric alpha-stable process is a symmetric Levy process in R^d with a Levy density given by c|x|^{-d-alpha} 1_{|x|< 1} for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality for nonnegative harmonic nonnegative functions these processes. We also establish a boundary Harnack principle for nonnegative functions which are harmonic with respect to these processes in bounded convex domains. We give an example of a non-convex domain for which the boundary Harnack principle fails.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-09-19T04:11:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J45"
    ],
    "keywords": [
      "potential theory",
      "truncated stable processes",
      "boundary harnack principle fails",
      "nonnegative functions",
      "symmetric levy process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5533K"
    }
  }
}