{
  "id": "2312.13548",
  "version": "v1",
  "published": "2023-12-21T03:19:01.000Z",
  "updated": "2023-12-21T03:19:01.000Z",
  "title": "Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces II: Sharp Boundedness of Almost Diagonal Operators",
  "authors": [
    "Fan Bu",
    "Tuomas Hytönen",
    "Dachun Yang",
    "Wen Yuan"
  ],
  "comment": "We split the article arXiv:2304.00292 into three articles and this is the second one",
  "categories": [
    "math.FA",
    "math.AP",
    "math.CA"
  ],
  "abstract": "This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, the authors obtain the sharp boundedness of almost diagonal operators on matrix-weighted Besov-type and Triebel--Lizorkin-type sequence spaces. These results not only possess broad generality but also improve most cases of existing almost diagonal conditions of matrix-weighted Besov and Triebel--Lizorkin sequence spaces and even also weighted Besov-type and Triebel--Lizorkin-type sequence spaces into sharp ones via using $A_p$-dimensions of matrix weights and their elaborate properties in terms of reducing operators obtained by the same authors in the first article of this series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-21T03:19:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "47A56",
      "42B25",
      "42B35"
    ],
    "keywords": [
      "matrix-weighted besov-type",
      "triebel-lizorkin-type spaces",
      "sharp boundedness",
      "diagonal operators",
      "triebel-lizorkin-type sequence spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}