{
  "id": "2307.10701",
  "version": "v1",
  "published": "2023-07-20T08:45:06.000Z",
  "updated": "2023-07-20T08:45:06.000Z",
  "title": "Discrete analogues of fractional integrals on product space",
  "authors": [
    "Jinhua Cheng"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "We study the discrete analogue of Stein-Weiss inequality and other variants of fractional integrals on product space, we prove some $\\ell^p\\rightarrow\\ell^q$ bounds for these operators via iteration methods and Fourier transform. In the last section, we involve a Dirichlet character in a discrete fractional integral, then prove the regularity theorem by Hardy-Littlewood circle method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-20T08:45:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "product space",
      "discrete analogue",
      "hardy-littlewood circle method",
      "discrete fractional integral",
      "regularity theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}