{
  "id": "1804.06296",
  "version": "v1",
  "published": "2018-04-17T14:47:34.000Z",
  "updated": "2018-04-17T14:47:34.000Z",
  "title": "Commutators of bilinear bi-parameter singular integrals",
  "authors": [
    "Kangwei Li",
    "Henri Martikainen",
    "Emil Vuorinen"
  ],
  "comment": "37 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study the boundedness properties of commutators formed by $b$ and $T$, where $T$ is a bilinear bi-parameter singular integral satisfying natural $T1$ type conditions and $b$ is a little BMO function. For paraproduct free bilinear bi-parameter singular integrals $T$ we prove that $[b, T]_1 \\colon L^p(\\mathbb{R}^{n+m}) \\times L^q(\\mathbb{R}^{n+m}) \\to L^r(\\mathbb{R}^{n+m})$ in the full range $1 < p, q \\le \\infty$, $1/2 < r < \\infty$ satisfying $1/p+1/q = 1/r$. A special case is when $T$ is a bilinear bi-parameter multiplier. We also prove the corresponding Banach range result for all singular integrals satisfying the $T1$ type conditions. In doing so we simplify the corresponding linear proof. Lastly, we prove analogous results for iterated commutators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-17T14:47:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "commutators",
      "free bilinear bi-parameter singular integrals",
      "paraproduct free bilinear bi-parameter singular",
      "type conditions",
      "bi-parameter singular integral satisfying natural"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}