{
  "id": "1910.01282",
  "version": "v1",
  "published": "2019-10-03T02:23:10.000Z",
  "updated": "2019-10-03T02:23:10.000Z",
  "title": "The Triangle Operator",
  "authors": [
    "Eyvindur A. Palsson",
    "Sean R. Sovine"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We examine the averaging operator corresponding to the manifold in $\\mathbb{R}^{2d}$ of pairs of points $(u,v)$ satisfying $|u| = |v| = |u - v| = 1$, so that $\\{0,u,v\\}$ is the set of vertices of an equilateral triangle. We establish $L^p \\times L^q \\rightarrow L^r$ boundedness for $T$ for $(1/p, 1/q, 1/r)$ in the convex hull of the set of points $\\lbrace (0, 0, 0) ,\\, (1, 0 , 1) ,\\, (0, 1, 1) , \\, ({1}/{p_d}, {1}/{p_d}, {2}/{p_d}) \\rbrace$, where $p_d = \\frac{5d}{3d - 2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-03T02:23:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "triangle operator",
      "convex hull",
      "equilateral triangle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}