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Lp estimates for the iterated Hardy-Littlewood maximal operator on\(\mathbb{R}^n \) and Kn, k a local fieldand Kn, k a local field

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Approximation Theory and its Applications

Abstract

In light of two measure estimate inequalities from [4] for the iterated Hardy-Littlewood maximal operatorMk f, certain equivalence betweenMk f and the Zygmund classLLogaL are established on\(\mathbb{R}^n \), so that we generalize Stein'sLLogL theorem. In Section 3, a simple induction enables us to prove such extensions onKn, the n-dimensional linear space over a local fieldK, without recoursing to Leckband's result.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, The University of New Mexico, 87131, Albuquerque, NM, USA

    Zheng Shijun

  2. Department of Mathematics, Nanjing University, 210093, Nanjing, P.R. of China

    W. Su

Authors
  1. Zheng Shijun
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  2. W. Su
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Supported by the NNSF, China

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Shijun, Z., Su, W. Lp estimates for the iterated Hardy-Littlewood maximal operator on\(\mathbb{R}^n \) and Kn, k a local fieldand Kn, k a local field. Approx. Theory & its Appl. 14, 36–54 (1998). https://doi.org/10.1007/BF02836766

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  • DOI: https://doi.org/10.1007/BF02836766

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