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The Tangential k-Cauchy–Fueter Operator on Right-Type Groups and Its Bochner–Martinelli Type Formula

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Abstract

The k-Cauchy–Fueter operator and the tangential k-Cauchy–Fueter operator are the quaternionic counterpart of Cauchy–Riemann operator and the tangential Cauchy–Riemann operator in the theory of several complex variables, respectively. In Wang (On the boundary complex of the k-Cauchy–Fueter complex, arXiv:2210.13656), Wang introduced the notion of right-type groups, which have the structure of nilpotent Lie groups of step-two, and many aspects of quaternionic analysis can be generalized to this kind of group. In this paper we generalize the right-type group to any step-two case, and introduce the generalization of Cauchy–Fueter operator on \({\mathbb {H}}^n\times {\mathbb {R}}^r.\) Then we establish the Bochner–Martinelli type formula for tangential k-Cauchy–Fueter operator on stratified right-type groups.

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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 of Science and Technology, Hangzhou, 310023, China

    Yun Shi

  2. Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310023, China

    Guangzhen Ren

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  1. Yun Shi
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  2. Guangzhen Ren
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Correspondence to Guangzhen Ren.

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Communicated by Wei Wang.

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The authors are supported by Nature Science Foundation of Zhejiang province (No. LY22A010013), National Nature Science Foundation in China (Nos. 11801508, 11971425, 12101564) and Domestic Visiting Scholar Teacher Professional Development Project (No. FX2021042).

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Shi, Y., Ren, G. The Tangential k-Cauchy–Fueter Operator on Right-Type Groups and Its Bochner–Martinelli Type Formula. Adv. Appl. Clifford Algebras 33, 22 (2023). https://doi.org/10.1007/s00006-023-01267-x

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