{
  "id": "1801.06865",
  "version": "v1",
  "published": "2018-01-21T18:16:37.000Z",
  "updated": "2018-01-21T18:16:37.000Z",
  "title": "Interpolation between H\\\" older and Lebesgue spaces with applications",
  "authors": [
    "Anastasia Molchanova",
    "Tomáš Roskovec",
    "Filip Soudský"
  ],
  "comment": "8 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Classical interpolation inequality of the type $\\|u\\|_{X}\\leq C\\|u\\|_{Y}^{\\theta}\\|u\\|_{Z}^{1-\\theta}$ is well known in the case when $X$, $Y$, $Z$ are Lebesgue spaces. In this paper we show that this result may be extended by replacing norms $\\|\\cdot\\|_{Y}$ or $\\|\\cdot\\|_{X}$ by suitable H\\\" older semi-norm. We shall even prove sharper version involving weak Lorentz norm. We apply this result to prove the Gagliardo--Nirenberg inequality for a wider scale of parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-21T18:16:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46E35"
    ],
    "keywords": [
      "lebesgue spaces",
      "applications",
      "weak lorentz norm",
      "wider scale",
      "classical interpolation inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}