{
  "id": "0706.0756",
  "version": "v1",
  "published": "2007-06-06T02:14:58.000Z",
  "updated": "2007-06-06T02:14:58.000Z",
  "title": "Boundedness of projection operators and Cesàro means in weighted $L^p$ space on the unit sphere",
  "authors": [
    "Feng Dai",
    "Yuan Xu"
  ],
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "For the weight function $\\prod_{i=1}^{d+1}|x_i|^{2\\k_i}$ on the unit sphere, sharp local estimates of the orthogonal projection operators are obtained and used to prove the convergence of the Ces\\`aro $(C,\\delta)$ means in the weighted $L^p$ space for $\\delta$ below the critical index. Similar results are also proved for corresponding weight functions on the unit ball and on the simplex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-06T02:14:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C50",
      "42B08",
      "42C10"
    ],
    "keywords": [
      "unit sphere",
      "cesàro means",
      "boundedness",
      "sharp local estimates",
      "orthogonal projection operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.0756D"
    }
  }
}