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The growth of H-harmonic functions on the Heisenberg group

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Abstract

We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group. Precisely, we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded. Moreover, we show that a class of H-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    HaiRong Liu, Long Tian & XiaoPing Yang

  2. School of Science, Nanjing Forestry University, Nanjing, 210037, China

    HaiRong Liu

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  1. HaiRong Liu
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  2. Long Tian
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  3. XiaoPing Yang
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Correspondence to HaiRong Liu.

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Liu, H., Tian, L. & Yang, X. The growth of H-harmonic functions on the Heisenberg group. Sci. China Math. 57, 795–806 (2014). https://doi.org/10.1007/s11425-013-4638-5

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