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The Tangential \(\varvec{k}\)-Cauchy–Fueter Operator and \(\varvec{k}\)-CF Functions Over the Heisenberg Group

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Abstract

In this paper, we investigate quaternionic analysis on the \((4n+1)\)-dimensional Heisenberg group. The tangential k-Cauchy–Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables, respectively. We give the Penrose integral formula for k-CF functions and establish the Bochner–Martinelli formula for the tangential k-Cauchy–Fueter operator. We also construct the tangential k-Cauchy–Fueter complex.

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Acknowledgements

The authors would like to thank the referees for many valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Guangzhen Ren & Wei Wang

  2. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, China

    Yun Shi

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  1. Guangzhen Ren
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  2. Yun Shi
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  3. Wei Wang
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Correspondence to Yun Shi.

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Guangzhen Ren and Yun Shi are partially supported by National Nature Science Foundation in China (Nos. 11571305, 11801508, 11971425); Wei Wang is partially supported by National Nature Science Foundation in China (Nos. 11571305, 11971425).

This article is part of the Topical Collection on ISAAC 12 at Aveiro, July 29–August 2, 2019, edited by Swanhild Bernstein, Uwe Kaehler, Irene Sabadini, and Franciscus Sommen.

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Ren, G., Shi, Y. & Wang, W. The Tangential \(\varvec{k}\)-Cauchy–Fueter Operator and \(\varvec{k}\)-CF Functions Over the Heisenberg Group. Adv. Appl. Clifford Algebras 30, 20 (2020). https://doi.org/10.1007/s00006-020-1043-3

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  • DOI: https://doi.org/10.1007/s00006-020-1043-3

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