{
  "id": "math/0610624",
  "version": "v1",
  "published": "2006-10-20T15:16:27.000Z",
  "updated": "2006-10-20T15:16:27.000Z",
  "title": "Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces",
  "authors": [
    "George Kyriazis",
    "Pencho Petrushev",
    "Yuan Xu"
  ],
  "comment": "34 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "The Littlewood-Paley theory is extended to weighted spaces of distributions on $[-1,1]$ with Jacobi weights $ \\w(t)=(1-t)^\\alpha(1+t)^\\beta. $ Almost exponentially localized polynomial elements (needlets) $\\{\\phi_\\xi\\}$, $\\{\\psi_\\xi\\}$ are constructed and, in complete analogy with the classical case on $\\RR^n$, it is shown that weighted Triebel-Lizorkin and Besov spaces can be characterized by the size of the needlet coefficients $\\{\\ip{f,\\phi_\\xi}\\}$ in respective sequence spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-20T15:16:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A38",
      "42B08",
      "42B15"
    ],
    "keywords": [
      "besov spaces",
      "weighted triebel-lizorkin",
      "jacobi decomposition",
      "respective sequence spaces",
      "littlewood-paley theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10624K"
    }
  }
}