{
  "id": "2009.06713",
  "version": "v1",
  "published": "2020-09-14T19:52:43.000Z",
  "updated": "2020-09-14T19:52:43.000Z",
  "title": "On weighted Hardy inequality with two-dimensional rectangular operator -- extension of the E. Sawyer theorem",
  "authors": [
    "V. D. Stepanov",
    "E. P. Ushakova"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A characterization is obtained for those pairs of weights $v$ and $w$ on $\\mathbb{R}^2_+$, for which the two--dimensional rectangular integration operator is bounded from a weighted Lebesgue space $L^p_v(\\mathbb{R}^2_+)$ to $L^q_w(\\mathbb{R}^2_+)$ for $1<p\\not= q<\\infty$, which is an essential complement to E. Sawyer's result \\cite{Saw1} given for $1<p\\leq q<\\infty$. Besides, we declare that the E. Sawyer theorem is actual if $p=q$ only, for $p<q$ the criterion is less complicated. The case $q<p$ is new.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-14T19:52:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional rectangular operator",
      "weighted hardy inequality",
      "sawyer theorem",
      "two-dimensional rectangular integration operator",
      "weighted lebesgue space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}