{
  "id": "2108.01146",
  "version": "v1",
  "published": "2021-08-02T19:51:38.000Z",
  "updated": "2021-08-02T19:51:38.000Z",
  "title": "$L^p$-$L^q$ Multipliers on commutative hypergroups",
  "authors": [
    "Vishvesh Kumar",
    "Michael Ruzhansky"
  ],
  "comment": "30 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2101.03416",
  "categories": [
    "math.FA"
  ],
  "abstract": "The main purpose of this paper is to prove H\\\"ormander's $L^p$-$L^q$ boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing Paley inequality and Hausdorff-Young-Paley inequality for commutative hypergroups. We show the $L^p$-$L^q$ boundedness of the spectral multipliers for the generalised radial Laplacian by examining our results on Ch\\'{e}bli-Trim\\`{e}che hypergroups. As a consequence, we obtain embedding theorems and time asymptotics for the $L^p$-$L^q$ norms of the heat kernel for generalised radial Laplacian. Finally, we present applications of the obtained results to study the well-posedness of nonlinear partial differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-02T19:51:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A62",
      "42B10",
      "42A45"
    ],
    "keywords": [
      "commutative hypergroups",
      "generalised radial laplacian",
      "nonlinear partial differential equations",
      "fourier multipliers",
      "main purpose"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}