{
  "id": "2407.10863",
  "version": "v1",
  "published": "2024-07-15T16:11:19.000Z",
  "updated": "2024-07-15T16:11:19.000Z",
  "title": "Fractional Hardy inequality with singularity on submanifold",
  "authors": [
    "Adimurthi",
    "Prosenjit Roy",
    "Vivek Sahu"
  ],
  "comment": "34 pages. arXiv admin note: text overlap with arXiv:2308.11956",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish fractional Hardy inequality on bounded domains in $\\mathbb{R}^{d}$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2, \\dots,d$, as weight function. The case $sp=k$ is the critical case, where optimal logarithmic corrections are required. All the other cases of $sp<k$ and $sp>k$ are also addressed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-15T16:11:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "26D15"
    ],
    "keywords": [
      "submanifold",
      "singularity",
      "establish fractional hardy inequality",
      "optimal logarithmic corrections",
      "weight function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}