{
  "id": "2303.13134",
  "version": "v1",
  "published": "2023-03-23T09:34:22.000Z",
  "updated": "2023-03-23T09:34:22.000Z",
  "title": "Pointwise multipliers for \\\\ Triebel--Lizorkin and Besov spaces on Lie groups",
  "authors": [
    "Tommaso Bruno",
    "Marco M. Peloso",
    "Maria Vallarino"
  ],
  "comment": "30 pages",
  "categories": [
    "math.FA",
    "math.AP",
    "math.CA"
  ],
  "abstract": "On a general Lie group $G$ endowed with a sub-Riemannian structure and of local dimension $d$, we characterize the pointwise multipliers of Triebel--Lizorkin spaces $F^{p,q}_{\\alpha}$ for $p,q\\in (1,\\infty)$ and $\\alpha>d/p$, and those of Besov spaces $B^{p,q}_{\\alpha}$ for $q\\in [1,\\infty]$, $p>d$ and $d/p< \\alpha<1$. When $G$ is stratified, we extend the latter characterization to all $p,q\\in [1,\\infty]$ and $\\alpha>d/p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-23T09:34:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "besov spaces",
      "pointwise multipliers",
      "general lie group",
      "sub-riemannian structure",
      "local dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}