Several Quaternionic Variables

In the literature there are several possible function theories of several quaternionic or Clifford variables. The first theory that was developed is the theory of several quaternionic variable based on Fueter regularity and in the same way also the theory of several Clifford variables was considered. With the development of the function theory of slice hyperholomorphic function in one variable it was clear that it was interesting to develop also the theory of several variables. For slice hyperholomorphic functions there are various possible definitions of regularity, that are not totally equivalent and this fact has implications in the case of several variables.