{
  "id": "2311.00828",
  "version": "v1",
  "published": "2023-11-01T20:22:30.000Z",
  "updated": "2023-11-01T20:22:30.000Z",
  "title": "Weighted weak-type inequalities for maximal operators and singular integrals",
  "authors": [
    "David Cruz-Uribe",
    "Brandon Sweeting"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional integral operators. We consider a kind of weak-type inequality that was first studied by Muckenhoupt and Wheeden and later by Cruz-Uribe, Martell and Perez. We obtain quantitative estimates for these operators in both the scalar and matrix weighted setting using sparse domination techniques. Our results extend those obtained by Cruz-Uribe, Isralowitz, Moen, Pott, and Rivera-R\\'ios for singular integrals and maximal operators when $p=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-01T20:22:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B35"
    ],
    "keywords": [
      "singular integrals",
      "weighted weak-type inequalities",
      "weak-type inequality",
      "fractional integral operators",
      "fractional maximal operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}