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

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.