{
  "id": "2402.13084",
  "version": "v2",
  "published": "2024-02-20T15:27:40.000Z",
  "updated": "2024-08-09T20:27:57.000Z",
  "title": "The Operator Norm of Paraproducts on Hardy Spaces",
  "authors": [
    "Shahaboddin Shaabani"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "For a tempered distribution \\( g \\), and \\( 0 < p, q, r < \\infty \\) with \\(\\frac{1}{q} = \\frac{1}{p} + \\frac{1}{r}\\), we show that the operator norm of a Fourier paraproduct \\(\\Pi_g\\), of the form \\[ \\Pi_{g}(f) := \\sum_{j \\in \\mathbb{Z}} (\\varphi_{2^{-j}} * f) \\cdot \\Delta_jg, \\] from \\( H^p(\\mathbb{R}^n) \\) to \\( \\dot{H}^q(\\mathbb{R}^n) \\) is comparable to \\( \\|g\\|_{\\dot{H}^r(\\mathbb{R}^n)} \\). We also establish a similar result for dyadic paraproducts acting on dyadic Hardy spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-08-09T20:27:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "operator norm",
      "dyadic hardy spaces",
      "similar result",
      "fourier paraproduct"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}