On non-homogeneous Cauchy–Fueter equations and Hartogs’ phenomenon in several quaternionic variables

Abstract

The Cauchy–Fueter complex is the counterpart of the Dolbeault complex in the theory of several quaternionic variables. By using the fundamental solution to the Laplacian operators of fourth order associated to this differential complex on H n , we can solve the system of non-homogeneous Cauchy–Fueter equations and prove the Hartogs’ extension phenomenon for quaternionic regular functions on any domain. The quaternionic version of Bochner–Martinelli integral representation formula for H -valued functions is also given.