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Sharp estimates of p-adic hardy and Hardy-Littlewood-Pólya operators

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Abstract

In this paper we get the sharp estimates of the p-adic Hardy and Hardy-Littlewood-Pólya operators on L q(|x| α p dx). Also, we prove that the commutators generated by the p-adic Hardy operators (Hardy-Littlewood-Pólya operators) and the central BMO functions are bounded on L q(|x| α p dx), more generally, on Herz spaces.

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Authors and Affiliations

  1. Department of Mathematics, Linyi University, Linyi, 276005, P. R. China

    Zun Wei Fu & Qing Yan Wu

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China

    Shan Zhen Lu

Authors
  1. Zun Wei Fu
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  2. Qing Yan Wu
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  3. Shan Zhen Lu
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Corresponding author

Correspondence to Qing Yan Wu.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 10901076, 10931001, 11126203 and 11171345), Natural Science Foundation of Shandong Province (Grant No. ZR2010AL006)

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Fu, Z.W., Wu, Q.Y. & Lu, S.Z. Sharp estimates of p-adic hardy and Hardy-Littlewood-Pólya operators. Acta. Math. Sin.-English Ser. 29, 137–150 (2013). https://doi.org/10.1007/s10114-012-0695-x

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  • DOI: https://doi.org/10.1007/s10114-012-0695-x

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