{
  "id": "1401.5457",
  "version": "v1",
  "published": "2014-01-21T20:44:56.000Z",
  "updated": "2014-01-21T20:44:56.000Z",
  "title": "Boundedness of non-homogeneous square functions and $L^q$ type testing conditions with $q \\in (1,2)$",
  "authors": [
    "Henri Martikainen",
    "Mihalis Mourgoglou"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We continue the study of local $Tb$ theorems for square functions defined in the upper half-space $(\\mathbb{R}^{n+1}_+, \\mu \\times dt/t)$. Here $\\mu$ is allowed to be a non-homogeneous measure in $\\mathbb{R}^n$. In this paper we prove a boundedness result assuming local $L^q$ type testing conditions in the difficult range $q \\in (1,2)$. Our theorem is a non-homogeneous version of a result of S. Hofmann valid for the Lebesgue measure. It is also an extension of the recent results of M. Lacey and the first named author where non-homogeneous local $L^2$ testing conditions have been considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-21T20:44:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "type testing conditions",
      "non-homogeneous square functions",
      "boundedness result assuming local",
      "upper half-space",
      "hofmann valid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.5457M"
    }
  }
}