{
  "id": "2009.05822",
  "version": "v1",
  "published": "2020-09-12T16:27:03.000Z",
  "updated": "2020-09-12T16:27:03.000Z",
  "title": "A New Inequality For The Hilbert Transform",
  "authors": [
    "Sakin Demir"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Suppose that $\\{a_j\\}\\in l^1$ has finite support. Then we prove that there is a constant $C$ such that $$\\sum_{n=1}^\\infty\\sharp\\left\\{k\\in\\mathbb{Z}:\\left| \\sum_{i=-n}^n \\! \\raise{1ex}\\hbox{${}'$} \\frac{a_{k+i}}{i} \\right| > \\lambda\\right\\} \\leq \\frac{C}{\\lambda}\\sum_{i=-\\infty}^\\infty |a_i|$$ for all $\\lambda>0$. We show as a corollary that one can use a transference argument to have an analogue result for the ergodic Hilbert transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-12T16:27:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D07",
      "47A35"
    ],
    "keywords": [
      "inequality",
      "ergodic hilbert transform",
      "transference argument",
      "finite support"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}