{
  "id": "2404.00329",
  "version": "v1",
  "published": "2024-03-30T11:48:54.000Z",
  "updated": "2024-03-30T11:48:54.000Z",
  "title": "Schatten classes and commutators in the two weight setting, II. Riesz transforms",
  "authors": [
    "Michael Lacey",
    "Ji Li",
    "Brett D. Wick",
    "Liangchuan Wu"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We characterize the Schatten class $S^p$ of the commutator of Riesz transforms $[b,R_j]$ in $\\mathbb R^n$ ($j=1,\\ldots, n$) in the two weight setting for $n< p<\\infty$, by introducing the condition that the symbol $b$ being in Besov spaces associated with the given two weights. At the critical index $p=n$, the commutator being in the weak Schatten class $S^{n,\\infty}$ is characterized by the symbol $b$ being in an oscillation sequence space associated with the given two weights. As a direct application, we have the Schatten class estimate for A. Connes' quantised derivative in the two weight setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-30T11:48:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riesz transforms",
      "weight setting",
      "commutator",
      "weak schatten class",
      "oscillation sequence space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}