{
  "id": "math/9208201",
  "version": "v1",
  "published": "1992-08-13T00:00:00.000Z",
  "updated": "1992-08-13T00:00:00.000Z",
  "title": "Vector-valued L_p convergence of orthogonal series and Lagrange interpolation",
  "authors": [
    "Hermann König",
    "Niels J. Nielsen"
  ],
  "journal": "Forum Math. 6 (1994), 183-207",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give necessary and sufficient conditions for interpolation inequalities of the type considered by Marcinkiewicz and Zygmund to be true in the case of Banach space-valued polynomials and Jacobi weights and nodes. We also study the vector-valued expansion problem of $L_p$-functions in terms of Jacobi polynomials and consider the question of unconditional convergence. The notion of type $p$ with respect to orthonormal systems leads to some characterizations of Hilbert spaces. It is also shown that various vector-valued Jacobi means are equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-08-13T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "46E40"
    ],
    "keywords": [
      "orthogonal series",
      "lagrange interpolation",
      "banach space-valued polynomials",
      "sufficient conditions",
      "jacobi weights"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math......8201K"
    }
  }
}