Fock and Hardy spaces: Clifford Appell case

In this paper, we study a specific system of Clifford–Appell polynomials and, in particular, their product. Moreover, introduce new family quaternionic reproducing kernel Hilbert spaces the framework Fueter regular functions. The construction is based on general idea which allows us to obtain various function by specifying suitable sequence real numbers. We focus Fock and Hardy cases setting, action mapping its range.