Based on our previous works concerning pseudo differential operators and their supersymmetric versions, we investigate to present an approach to interpret some results concerning the mapping between two superconformal field theories. As a direct result, we have reduced the number of super fields which parametrizes [Formula: see text] super W3-algebra theory. Such a decomposition can be interpreted physically as the interaction between a fermionic particle of conformal spin [Formula: see text] and a bosonic particle of spin [Formula: see text] ([Formula: see text], [Formula: see text] or [Formula: see text] for example) given rise to supersymmetric particles of total conformal spin [Formula: see text].