{
  "id": "2410.13438",
  "version": "v1",
  "published": "2024-10-17T11:08:08.000Z",
  "updated": "2024-10-17T11:08:08.000Z",
  "title": "Universal multipliers for Sub-Hardy Hilbert spaces",
  "authors": [
    "Bartosz Malman",
    "Daniel Seco"
  ],
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "To every non-extreme point $b$ of the unit ball of $\\hil^\\infty$ of the unit disk there corresponds a Pythagorean mate, a bounded outer function $a$ satisfying the equation $|a|^2 + |b|^2 = 1$ on the boundary of the disk. We study universal, i.e., simultaneous multipliers for families of de Branges-Rovnyak spaces $\\hb$, and develop a general framework for this purpose. Our main results include a new proof of the Davis-McCarthy universal multiplier theorem for the class of all non-extreme spaces $\\hb$, a characterization of the Lipschitz classes as the universal multipliers for spaces $\\hb$ for which the quotient $b/a$ is contained in a Hardy space, and a similar characterization of the Gevrey classes as the universal multipliers for spaces $\\hb$ for which $b/a$ is contained in a Privalov class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-17T11:08:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30H45",
      "47B32"
    ],
    "keywords": [
      "sub-hardy hilbert spaces",
      "davis-mccarthy universal multiplier theorem",
      "privalov class",
      "hardy space",
      "pythagorean mate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}