{
  "id": "1109.3676",
  "version": "v2",
  "published": "2011-09-16T17:55:59.000Z",
  "updated": "2012-01-24T16:21:19.000Z",
  "title": "On harmonic functions of symmetric Levy processes",
  "authors": [
    "Ante Mimica"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider some classes of Levy processes for which the estimate of Krylov and Safonov (as in [BL02]) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Holder continuity estimates of harmonic functions. Despite the faliure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processes. Moreover, we extend results from [SSV06] and obtain asymptotic behavior of the Green function and the Levy density for a large class of subordinate Brownian motions, where the Laplace exponent of the corresponding subordinator is a slowly varying function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-24T16:21:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic functions",
      "symmetric levy processes",
      "a-priori holder continuity estimates",
      "standard iteration technique",
      "a-priori regularity estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.3676M"
    }
  }
}