{
  "id": "math/0605307",
  "version": "v1",
  "published": "2006-05-11T17:31:02.000Z",
  "updated": "2006-05-11T17:31:02.000Z",
  "title": "A Simple Proof of Inequalities of Integrals of Composite Functions",
  "authors": [
    "Zhenglu Jiang",
    "Xiaoyong Fu",
    "Hongjiong Tian"
  ],
  "journal": "Journal of Mathematical Analysis and Applications, Vol 332, Number 2, 2007, p1308-1313.",
  "doi": "10.1016/j.jmaa.2006.11.007",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continous convex functions on a vector space ${\\bf R}^m$ and vector-valued functions in a weakly compact subset of a Banach vector space generated by $m$ $L_\\mu^p$-spaces for $1\\leq p<+\\infty.$ Also, the same inequalities hold if these vector-valued functions are in a weakly* compact subset of a Banach vector space generated by $m$ $L_\\mu^\\infty$-spaces instead.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-11T17:31:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple proof",
      "composite functions",
      "banach vector space",
      "vector-valued functions",
      "inequalities hold"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Mathematical Analysis and Applications",
      "year": 2007,
      "month": "Aug",
      "volume": 332,
      "number": 2,
      "pages": 1308
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007JMAA..332.1308J"
    }
  }
}