{
  "id": "2408.07775",
  "version": "v1",
  "published": "2024-08-14T19:05:55.000Z",
  "updated": "2024-08-14T19:05:55.000Z",
  "title": "Sharp quantitative stability estimates for critical points of fractional Sobolev inequalities",
  "authors": [
    "Haixia Chen",
    "Seunghyeok Kim",
    "Juncheng Wei"
  ],
  "comment": "36 pages; comments welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates for critical points of the fractional Sobolev inequalities induced by the embedding $\\dot{H}^s({\\mathbb R}^n) \\hookrightarrow L^{2n \\over n-2s}({\\mathbb R}^n)$ in the whole range of $s \\in (0,\\frac{n}{2})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-14T19:05:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional sobolev inequalities",
      "critical points",
      "establish sharp quantitative stability estimates",
      "integral representations",
      "unified approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}