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Hausdorff operators on the Heisenberg group

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Abstract

This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group Hn. The sharp bounds for the strong type (p, p) (1 ≤ p ≤ ∞) estimates of n-dimensional Hausdorff operators on Hn are obtained. The sharp bounds for strong (p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on Hn. The weak type (p, p) (1 ≤ p≤∞) estimates are also obtained. Keywords Hausdorff operator, Heisenberg group, multilinear, sharp estimate

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    Jiu Hua Guo

  2. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, 53201, USA

    Li Jing Sun

  3. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    Fa You Zhao

Authors
  1. Jiu Hua Guo
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  2. Li Jing Sun
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  3. Fa You Zhao
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Correspondence to Fa You Zhao.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11201287) and China Scholarship Council (Grant No. 201406895019)

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Guo, J.H., Sun, L.J. & Zhao, F.Y. Hausdorff operators on the Heisenberg group. Acta. Math. Sin.-English Ser. 31, 1703–1714 (2015). https://doi.org/10.1007/s10114-015-5109-4

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  • DOI: https://doi.org/10.1007/s10114-015-5109-4

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