{
  "id": "1701.08922",
  "version": "v1",
  "published": "2017-01-31T05:32:09.000Z",
  "updated": "2017-01-31T05:32:09.000Z",
  "title": "Hardy-Littlewood inequalities on compact quantum groups of Kac type",
  "authors": [
    "SangGyun Youn"
  ],
  "comment": "22 pages",
  "categories": [
    "math.OA"
  ],
  "abstract": "The Hardy-Littlewood inequality on $\\mathbb{T}$ compares the $L^p$-norm of a function with a weighted $\\ell^p$-norm of its Fourier coefficients. The approach has recently been studied for compact homogeneous spaces and we study a natural analogue in the framework of compact quantum groups. Especially, in the case of the reduced group $C^*$-algebras and free quantum groups, we establish explicit $L^p-\\ell^p$ inequalities through inherent information of underlying quantum group, such as growth rate and rapid decay property. Moreover, we show sharpness of the inequalities in a large class, including $C(G)$ with compact Lie group, $C_r^*(G)$ with polynomially growing discrete group and free quantum groups $O_N^+$, $S_N^+$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-31T05:32:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G42",
      "46L52"
    ],
    "keywords": [
      "compact quantum groups",
      "hardy-littlewood inequality",
      "kac type",
      "free quantum groups",
      "compact lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}