{
  "id": "2108.00656",
  "version": "v1",
  "published": "2021-08-02T06:28:26.000Z",
  "updated": "2021-08-02T06:28:26.000Z",
  "title": "Parabolic weighted Sobolev-Poincaré type inequalities",
  "authors": [
    "Lars Diening",
    "Mikyoung Lee",
    "Jihoon Ok"
  ],
  "comment": "12pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive weighted Sobolev-Poincar\\'e type inequalities in function spaces concerned with parabolic partial differential equations. We consider general weights depending on both space and time variables belonging to a Muckenhoupt class, so-called the parabolic $A_p$-class, where only the parabolic cubes are involved in the definition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-02T06:28:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic partial differential equations",
      "derive weighted sobolev-poincare type inequalities",
      "function spaces",
      "muckenhoupt class",
      "parabolic cubes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}