{
  "id": "1708.05578",
  "version": "v1",
  "published": "2017-08-18T12:28:45.000Z",
  "updated": "2017-08-18T12:28:45.000Z",
  "title": "Bohr's inequality for analytic functions $\\sum_k b_k z^{kp+m}$ and harmonic functions",
  "authors": [
    "Ilgiz R Kayumov",
    "Saminathan Ponnusamy"
  ],
  "comment": "13 pages; The article is with a journal for several months",
  "categories": [
    "math.CV"
  ],
  "abstract": "We determine the Bohr radius for the class of all functions $f$ of the form $f(z)=\\sum_{k=1}^\\infty a_{kp+m} z^{kp+m}$ analytic in the unit disk $|z|<1$ and satisfy the condition $|f(z)|\\le 1$ for all $|z|<1$. In particular, our result also contains a solution to a recent conjecture of Ali, Barnard and Solynin \\cite{AliBarSoly} for the Bohr radius for odd analytic functions, solved by the authors in \\cite{KayPon1}. We consider a more flexible approach by introducing the $p$-Bohr radius for harmonic functions which in turn contains the classical Bohr radius as special case. Also, we prove several other new results and discuss $p$-Bohr radius for the class of odd harmonic bounded functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-18T12:28:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30A05",
      "30A10",
      "30B10",
      "30H05",
      "41A58",
      "40A30"
    ],
    "keywords": [
      "harmonic functions",
      "bohrs inequality",
      "odd analytic functions",
      "odd harmonic bounded functions",
      "unit disk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}