{
  "id": "1902.00899",
  "version": "v1",
  "published": "2019-02-03T14:10:38.000Z",
  "updated": "2019-02-03T14:10:38.000Z",
  "title": "Series expansion of weighted Finsler-Kato-Hardy inequalities",
  "authors": [
    "Konstantinos Tzirakis"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work, we consider weighted anisotropic Hardy inequalities and trace Hardy inequalities involving a general Finsler metric. We follow a unifying approach, by establishing first a sharp interpolation between them, extending the corresponding nonweighted version, being established recently by a different approach. Then, passing to bounded domains, we obtain successive sharp improvements by adding remainder terms involving sharp weights and optimal constants, resulting in an infinite series-type improvement. The results extend, into the Finsler context, the earlier known ones within the Euclidean setting. The generalization of our results to cones is also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-03T14:10:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "26D10",
      "46E35"
    ],
    "keywords": [
      "weighted finsler-kato-hardy inequalities",
      "series expansion",
      "trace hardy inequalities",
      "general finsler metric",
      "infinite series-type improvement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}