{
  "id": "2401.06434",
  "version": "v1",
  "published": "2024-01-12T07:58:02.000Z",
  "updated": "2024-01-12T07:58:02.000Z",
  "title": "On Fractional Orlicz-Hardy Inequalities",
  "authors": [
    "T. V. Anoop",
    "Prosenjit Roy",
    "Subhajit Roy"
  ],
  "comment": "24 pages, 3 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the weighted fractional Orlicz-Hardy inequalities for various Orlicz functions. Further, we identify the critical cases for each Orlicz function and prove the weighted fractional Orlicz-Hardy inequalities with logarithmic correction. Moreover, we discuss the analogous results in the local case. In the process, for any Orlicz function $\\Phi$ and for any $\\Lambda>1$, the following inequality is established $$ \\Phi(a+b)\\leq \\lambda\\Phi(a)+\\frac{C( \\Phi, \\Lambda )}{(\\lambda-1)^{p_\\Phi^+-1}}\\Phi(b),\\;\\;\\;\\forall\\,a,b\\in [0,\\infty),\\,\\forall\\,\\lambda\\in (1,\\Lambda], $$ where $p_\\Phi^+:=\\sup\\big\\{t\\varphi(t)/\\Phi(t):t>0\\big\\},$ $\\varphi$ is the right derivatives of $\\Phi$ and $C( \\Phi, \\Lambda )$ is a positive constant that depends only on $\\Phi$ and $\\Lambda.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-12T07:58:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "35R11",
      "35A23"
    ],
    "keywords": [
      "inequality",
      "weighted fractional orlicz-hardy inequalities",
      "orlicz function",
      "logarithmic correction",
      "right derivatives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}