{
  "id": "1005.1842",
  "version": "v1",
  "published": "2010-05-11T14:23:02.000Z",
  "updated": "2010-05-11T14:23:02.000Z",
  "title": "$L^\\infty$ to $L^p$ constants for Riesz projections",
  "authors": [
    "Jordi Marzo",
    "Kristian Seip"
  ],
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "The norm of the Riesz projection from $L^\\infty(\\T^n)$ to $L^p(\\T^n)$ is considered. It is shown that for $n=1$, the norm equals $1$ if and only if $p\\le 4$ and that the norm behaves asymptotically as $p/(\\pi e)$ when $p\\to \\infty$. The critical exponent $p_n$ is the supremum of those $p$ for which the norm equals $1$. It is proved that $2+2/(2^n-1)\\le p_n <4$ for $n>1$; it is unknown whether the critical exponent for $n=\\infty$ exceeds $2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-11T14:23:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A44",
      "42B05",
      "46E30"
    ],
    "keywords": [
      "riesz projection",
      "norm equals",
      "critical exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1842M"
    }
  }
}