{
  "id": "2102.04748",
  "version": "v1",
  "published": "2021-02-09T10:34:13.000Z",
  "updated": "2021-02-09T10:34:13.000Z",
  "title": "New estimates for the maximal functions and applications",
  "authors": [
    "Oscar Domínguez",
    "Sergey Tikhonov"
  ],
  "comment": "47 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore's inequality for the moduli of smoothness and a logarithmic variant of Bennett--DeVore--Sharpley's inequality for rearrangements. As a consequence, we improve the classical Stein--Zygmund embedding deriving $\\dot{B}^{d/p}_\\infty L_{p,\\infty}(\\mathbb{R}^d) \\hookrightarrow \\text{BMO}(\\mathbb{R}^d)$ for $1 < p < \\infty$. Moreover, these results are also applied to establish new Fefferman--Stein inequalities, Calder\\'on--Scott type inequalities, and extrapolation estimates. Our approach is based on the limiting interpolation techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-09T10:34:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "42B35",
      "26A15",
      "46E30",
      "46B70"
    ],
    "keywords": [
      "maximal functions",
      "applications",
      "study sharp pointwise inequalities",
      "calderon-scott type inequalities",
      "strengthen devores inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}