{
  "id": "1805.10935",
  "version": "v1",
  "published": "2018-05-28T14:19:44.000Z",
  "updated": "2018-05-28T14:19:44.000Z",
  "title": "Optimal non-homogeneous improvements for the series expansion of Hardy's inequality",
  "authors": [
    "Konstantinos T. Gkikas",
    "Georgios Psaradakis"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the series expansion of the $L^p$-Hardy inequality of \\cite{BFT2}, in the particular case where the distance is taken from an interior point of a bounded domain in $\\mathbb{R}^n$ and $1<p\\neq n$. For $p<n$ we improve it by adding as a remainder term an optimally weighted critical Sobolev norm, generalizing the $p=2$ result of \\cite{FT} and settling the open question raised in \\cite{BFT1}. For $p>n$ we improve it by adding as a remainder term the optimally weighted H\\\"{o}lder seminorm, extending the Hardy-Morrey inequality of \\cite{Ps} to the series case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-28T14:19:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal non-homogeneous improvements",
      "series expansion",
      "hardys inequality",
      "weighted critical sobolev norm",
      "remainder term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}