{
  "id": "2001.06165",
  "version": "v1",
  "published": "2020-01-17T06:38:06.000Z",
  "updated": "2020-01-17T06:38:06.000Z",
  "title": "On the stability of the Lions-Peetre method of real interpolation with functional parameter",
  "authors": [
    "Amiran Gogatishvili"
  ],
  "categories": [
    "math.FA",
    "math.AP",
    "math.CA"
  ],
  "abstract": "Let $\\vec{X}=(X_0, X_1)$ be a compatible couple of Banach spaces, $ 1\\le p \\le \\infty$ and let $ \\varphi$ be positive quasi-concave function. Denote by $\\overline{X}_{\\varphi,p}=(X_0,X_1)_{\\varphi,p}$ the real interpolation spaces defined by S. Janson (1981). We give necessary and sufficient conditions on $ \\varphi_{0}$, $\\varphi_{1}$ and $\\varphi$ for the validity of \\begin{equation*} \\left(\\overline{X}_{\\varphi_{0},1},\\overline{X}_{\\varphi_{1},1} \\right) _{\\varphi,p}= \\left(\\overline{X}_{\\varphi_{0},\\infty},\\overline{X}_{\\varphi_{1},\\infty}\\right)_{\\varphi,p} \\end{equation*} for all $ 1\\le p\\le \\infty$, and all Banach couples $\\overline{X}. $",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-17T06:38:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B70",
      "46M35",
      "46E30"
    ],
    "keywords": [
      "lions-peetre method",
      "functional parameter",
      "real interpolation spaces",
      "banach spaces",
      "banach couples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}