Recently one of the authors has introduced the concept of generalized Poisson functionals and discussed the differentiation, renormalization, stochastic integrals etc. (, ), analogously to the works of T. Hida (, , ). Here we introduce a transformation for Poisson fnnctionals with the idea as in the case of Gaussian white noise (cf. , , , ). Then we can discuss the differentiation, renormalization, multiple Wiener integrals etc. in a way completely parallel with the Gaussian case. The only one exceptional point, which is most significant, is that the multiplications are described by
for the Gaussian case,
for the Poisson case,
as will be stated in Section 5. Conversely, those formulae characterize the types of white noises.