{
  "id": "2208.11775",
  "version": "v1",
  "published": "2022-08-24T21:15:26.000Z",
  "updated": "2022-08-24T21:15:26.000Z",
  "title": "The ε-Maximal Operator and Haar Multipliers on Variable Lebesgue Spaces",
  "authors": [
    "David Cruz-Uribe",
    "Michael Penrod"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "C. Stockdale, P. Villarroya, and B. Wick introduced the $\\epsilon$-maximal operator to prove the Haar multiplier is bounded on the weighted spaces $L^p(w)$ for a class of weights larger than $A_p$. We prove the $\\epsilon$-maximal operator and Haar multiplier are bounded on variable Lebesgue spaces $\\Lpp(\\R^n)$ for a larger collection of exponent functions than the log-Holder continuous functions used to prove the boundedness of the maximal operator on $\\Lpp(\\R^n)$. We also prove that the Haar multiplier is compact when restricted to a dyadic cube $Q_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-24T21:15:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42B25",
      "42A45"
    ],
    "keywords": [
      "haar multiplier",
      "variable lebesgue spaces",
      "maximal operator",
      "weights larger",
      "larger collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}