We construct the tangential k-Cauchy–Fueter complexes on the right quaternionic Heisenberg group, as the quaternionic counterpart of \(\overline{\partial }_b\)-complex on the Heisenberg group in the theory of several complex variables. We can use the \(L^2\) estimate to solve the nonhomogeneous tangential k-Cauchy–Fueter equation under the compatibility condition over this group modulo a lattice. This solution has an important vanishing property when the group is higher dimensional. It allows us to prove the Hartogs’ extension phenomenon for k-CF functions, which are the quaternionic counterpart of CR functions.

我们在几个复变数的理论上，在右四元数的Heisenberg群上构造切向k -Cauchy-Fueter复数，作为Heisenberg群上的\（\ overline {\ partial} _b \） -复数的四元数对应物。我们可以使用\（L ^ 2 \）估计来求解在相容条件下该组模的非齐次切向k -Cauchy–Fueter方程。当组的维数较高时，此解决方案具有重要的消失特性。它使我们能够证明k -CF函数的Hartogs扩展现象，这是CR函数的四元数对应物。