{
  "id": "1909.09322",
  "version": "v1",
  "published": "2019-09-20T04:49:53.000Z",
  "updated": "2019-09-20T04:49:53.000Z",
  "title": "Integral operators with rough kernels in variable Lebesgue spaces",
  "authors": [
    "Marta Urciuolo",
    "Lucas Vallejos"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we study integral operators with kernels \\begin{equation*} K(x,y)= k_1( x- A_1y)...k_m( x-A_my), \\end{equation*} $k_i(x)=\\frac{\\Omega_i(x)}{|x|^{n/q_i}}$ where $\\Omega_i: \\mathbb{R}^n\\to \\mathbb{R}$ are homogeneous functions of degree zero, satisfying a size and a Dini condition, $A_{i}$ are certain invertible matrices, and $\\frac n{q_1}+\\dots\\frac n{q_m}=n-\\alpha,$ $0\\leq \\alpha <n.$ We obtain the boundedness of this operator from $L^{p(\\cdot)}$ into $% L^{q(\\cdot)}$ for $\\frac{1}{q(\\cdot)}=\\frac{1}{p(\\cdot)}-\\frac{\\alpha }{n},$ for certain exponent functions $p$ satisfying weaker conditions than the classical log-H\\\"older conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-20T04:49:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B35"
    ],
    "keywords": [
      "variable lebesgue spaces",
      "rough kernels",
      "study integral operators",
      "satisfying weaker conditions",
      "exponent functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}