{
  "id": "1504.04408",
  "version": "v1",
  "published": "2015-04-16T23:40:58.000Z",
  "updated": "2015-04-16T23:40:58.000Z",
  "title": "Operator-valued Fourier multipliers on periodic Besov spaces",
  "authors": [
    "Bienvenido Barraza Martínez",
    "Ivan González Martínez",
    "Jairo Hernández Monzón"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove in this paper that a sequence $M:\\mathbb{Z}^{n}\\to\\mathcal{L}(E)$ of bounded variation is a Fourier multiplier on the Besov space $B_{p,q}^{s}(\\mathbb{T}^{n},E)$ for $s\\in\\mathbb{R}$, $1<p<\\infty$, $1\\leq q\\leq\\infty$ and $E$ a Banach space, if and only if $E$ is a UMD-space. This extends in some sense the Theorem 4.2 in [AB04] to the $n-$dimensional case. The result is used to obtain existence and uniqueness of solution for some Cauchy problems with periodic boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-16T23:40:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic besov spaces",
      "operator-valued fourier multipliers",
      "periodic boundary conditions",
      "dimensional case",
      "cauchy problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150404408B"
    }
  }
}