{
  "id": "0902.2928",
  "version": "v1",
  "published": "2009-02-17T14:29:15.000Z",
  "updated": "2009-02-17T14:29:15.000Z",
  "title": "Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones",
  "authors": [
    "D. Békollé",
    "A. Bonami",
    "G. Garrigós",
    "F. Ricci",
    "B. Sehba"
  ],
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "We give various equivalent formulations to the (partially) open problem about $L^p$-boundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, $A^{p'}=(A^p)^*$, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequalities play an important role. For $p\\geq 2$ we identify as a Besov space the range of the Bergman projection acting on $L^p$, and also the dual of $A^{p'}$. For the Bloch space $\\SB^\\infty$ we give in addition new necessary conditions on the number of derivatives required in its definition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-17T14:29:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "32M15"
    ],
    "keywords": [
      "analytic besov spaces",
      "tube domains",
      "hardy-type inequalities",
      "symmetric cones",
      "bergman projection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2928B"
    }
  }
}