{
  "id": "0812.0982",
  "version": "v1",
  "published": "2008-12-04T16:58:12.000Z",
  "updated": "2008-12-04T16:58:12.000Z",
  "title": "Regularity results for stable-like operators",
  "authors": [
    "Richard F. Bass"
  ],
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "For $\\alpha\\in [1,2)$ we consider operators of the form $$L f(x)=\\int_{R^d} [f(x+h)-f(x)-1_{(|h|\\leq 1)} \\nabla f(x)\\cdot h] \\frac{A(x,h)}{|h|^{d+\\alpha}}$$ and for $\\alpha\\in (0,1)$ we consider the same operator but where the $\\nabla f$ term is omitted. We prove, under appropriate conditions on $A(x,h)$, that the solution $u$ to $L u=f$ will be in $C^{\\alpha+\\beta}$ if $f\\in C^\\beta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-04T16:58:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "45K05",
      "35B65",
      "60J75"
    ],
    "keywords": [
      "regularity results",
      "stable-like operators",
      "appropriate conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.0982B"
    }
  }
}