{
  "id": "2209.07998",
  "version": "v1",
  "published": "2022-09-16T15:25:39.000Z",
  "updated": "2022-09-16T15:25:39.000Z",
  "title": "The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary Hölder Regularity",
  "authors": [
    "Anatoly N. Kochubei"
  ],
  "categories": [
    "math.AP",
    "math.FA",
    "math.NT"
  ],
  "abstract": "We study the Vladimirov-Taibleson operator, a model example of a pseudo-differential operator acting on real- or complex-valued functions defined on a non-Archimedean local field. We prove analogs of classical inequalities for fractional Laplacian, study the counterpart of the Dirichlet problem including the property of boundary H\\\"older regularity of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-16T15:25:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S05",
      "11S80",
      "47G30",
      "35S11",
      "35R11"
    ],
    "keywords": [
      "boundary hölder regularity",
      "vladimirov-taibleson operator",
      "dirichlet problem",
      "inequalities",
      "non-archimedean local field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}