{
  "id": "2311.05974",
  "version": "v1",
  "published": "2023-11-10T10:14:22.000Z",
  "updated": "2023-11-10T10:14:22.000Z",
  "title": "New Characterizations and Properties of Matrix $A_\\infty$ Weights",
  "authors": [
    "Fan Bu",
    "Tuomas Hytönen",
    "Dachun Yang",
    "Wen Yuan"
  ],
  "comment": "39 pages. arXiv admin note: text overlap with arXiv:2304.00292",
  "categories": [
    "math.FA"
  ],
  "abstract": "We provide several new characterizations of $A_{p,\\infty}$-matrix weights, originally introduced by A. Volberg as matrix-valued substitutes of the classical $A_\\infty$ weights. In analogy with the notion of $A_p$-dimension of matrix weights introduced in our previous work, we introduce the concepts of the lower and the upper dimensions of $A_{p,\\infty}$-matrix weights, which enable us to obtain sharp estimates related to their reducing operators. In a follow-up work, these results will play a key role in the study of function spaces with $A_{p,\\infty}$-matrix weights, which extends earlier results in the more restricted class of $A_p$-matrix weights.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-10T10:14:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "47A56",
      "15A15",
      "42B35"
    ],
    "keywords": [
      "matrix weights",
      "characterizations",
      "properties",
      "extends earlier results",
      "upper dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}