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On fundamental solution for powers of the sub-Laplacian on the Heisenberg group

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Abstract

We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and to construct its fundamental solution. Besides, the series representation of the fundamental solution for square of the sub-Laplacian on the Heisenberg group is given and we also get the closed form of the fundamental solution for square of the sub-Laplacian on the Heisenberg group with dimension n = 2, 3, 4.

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Authors and Affiliations

  1. School of Mathematics and Information Technology, Jiangsu Second Normal University, Nanjing, 210013, China

    Hai-meng Wang

  2. School of Science, Linyi University, Linyi, 276000, China

    Qing-yan Wu

Authors
  1. Hai-meng Wang
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  2. Qing-yan Wu
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Correspondence to Hai-meng Wang.

Additional information

Supported by Doctor Special Foundation of Jiangsu Second Normal University (JSNU2015BZ07).

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Wang, Hm., Wu, Qy. On fundamental solution for powers of the sub-Laplacian on the Heisenberg group. Appl. Math. J. Chin. Univ. 32, 365–378 (2017). https://doi.org/10.1007/s11766-017-3506-4

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  • DOI: https://doi.org/10.1007/s11766-017-3506-4

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