{
  "annotation_id": "d26bd70c-e638-49ee-897b-8cfd652c2ab7",
  "date_created": "2026-02-17T05:53:19.908000Z",
  "date_modified": "2026-02-17T05:53:19.908000Z",
  "file_hash": "fe0a1fb21dc56ce7d4e4263843fcb12d5fc21f315b9cdf2bd35f4581f2cc9e02",
  "private": false,
  "record": {
    "abstract": "We show that a bilinear radial Fourier multiplier operator with symbol $\\sigma$ is $L^2(\\R^n)\\times L^2(\\R^n) \\to L^1(\\R^n)$ bounded, $n\\in \\mathbb N,$ if the function $\\sigma$ satisfies the smoothness condition $\\sigma(2^j\\cdot)\\Phi\\in L^2_{1/2 +\\epsilon}(\\mathbb R^{2n})$ for some $\\epsilon\u003e0$ and every $j\\in \\mathbb Z,$ where $\\Phi$ is a smooth cutoff function adapted to the annulus $|x|\\in [1/4,4]$. This condition is dimension free. We also apply similar reasoning to provide alternative proof of the initial result concerning multilinear Bochner-Riesz operator and prove an estimate for generalized bilinear Bochner-Riesz operator.",
    "arxiv_id": "2601.09412",
    "authors": [
      "Petr Honz\u00edk",
      "Maty\u00e1\u0161 Male\u010dek"
    ],
    "categories": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Boundedness of bilinear radial Fourier multipliers",
    "url": "https://arxiv.org/abs/2601.09412",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9f047139-bcf1-4a93-9ed7-57b64f256969",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}