{
  "id": "math/0311360",
  "version": "v2",
  "published": "2003-11-20T20:57:50.000Z",
  "updated": "2003-11-20T21:13:16.000Z",
  "title": "Interpolating sequences for the Bergman space and the $\\bar\\partial$-equation in weighted $L^p$",
  "authors": [
    "Daniel H. Luecking"
  ],
  "comment": "23pages",
  "categories": [
    "math.CV"
  ],
  "abstract": "The author showed that a sequence in the unit disk is a zero sequence for the Bergman space $A^p$ if and only if a certain weighted space $L^p(W}$ contains a nontrivial analytic function. In this paper it is shown that the sequence is an interpolating sequence for $A^p$ if and only if it is separated in the hyperbolic metric and the $\\bar\\partial$-equation $(1 - |z|^2)\\bar\\partial u = f$ has a solution $u$ belonging to $L^p(W)$ for every $f$ in $L^p(W)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-11-20T21:13:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30H05",
      "30E05",
      "46E20"
    ],
    "keywords": [
      "bergman space",
      "interpolating sequence",
      "nontrivial analytic function",
      "hyperbolic metric",
      "unit disk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11360L"
    }
  }
}