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.

中文翻译：

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Heisenberg群上的切向$$ \ varvec {k} $$ k -Cauchy–Fueter运算符和$$ \ varvec {k} $$ k -CF函数

在本文中，我们研究了\（（4n + 1）\）维Heisenberg群的四元数分析。在多个复杂变量的理论中，切向k -Cauchy-Fueter算子和k -CF函数分别对应于Heisenberg群上的切向Cauchy-Riemann算子和CR函数。我们给出k -CF函数的Penrose积分公式，并建立正切k -Cauchy-Fueter算子的Bochner-Martinelli公式。我们还构造了切向k -Cauchy-Fueter复数。