{
  "id": "2205.02504",
  "version": "v1",
  "published": "2022-05-05T08:27:23.000Z",
  "updated": "2022-05-05T08:27:23.000Z",
  "title": "Hardy-Littlewood-type theorems for Fourier transforms in $\\R^d$",
  "authors": [
    "Mikhail Dyachenko",
    "Erlan Nursultanov",
    "Sergey Tikhonov",
    "Ferenc Weisz"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\\infty$ involving the Hardy-Ces\\`aro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\\le 1$. Moreover, boundedness of the Hardy-Ces\\`aro and Hardy-Bellman operators in various spaces (Lebesgue, Hardy, BMO) is discussed. One of our main tools is an appropriate version of the Hardy-Littlewood-Paley inequality $ \\|\\widehat{f}\\|_{L_{p',q}} \\lesssim \\left\\|f\\right\\|_{L_{p,q}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-05T08:27:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42A38",
      "42B30"
    ],
    "keywords": [
      "fourier transforms",
      "hardy-littlewood-type theorems",
      "hardy-bellman operators",
      "product hardy spaces",
      "hardy-littlewood-paley inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}