{
  "id": "1612.07160",
  "version": "v1",
  "published": "2016-12-21T15:00:43.000Z",
  "updated": "2016-12-21T15:00:43.000Z",
  "title": "Martingale Inequalities in Variable Exponent Hardy spaces with $0<p^-\\leq p^+<\\infty$",
  "authors": [
    "Peide Liu",
    "Wei Chen"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate the properties of the variable Lebesgue spaces with quasi-norm on a probability space, and give the atomic decompositions suited to the variable exponent martingale Hardy spaces. Using the decompositions and the harmonic mean of a variable exponent, we obtain several continuous embedding relations between martingale Hardy spaces with small exponent. Finally, we extend these results to the cases $0<p^-\\leq p^+<\\infty.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-21T15:00:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G46",
      "60G42"
    ],
    "keywords": [
      "variable exponent hardy spaces",
      "martingale inequalities",
      "variable exponent martingale hardy spaces",
      "atomic decompositions",
      "variable lebesgue spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}