  In this paper we study the regularity properties of linear and polynomial
images of Skorohod differentiable measures. Firstly, we obtain estimates for
the Skorohod derivative norm of a projection of a product of Scorohod
differentiable measures. In the second part of the paper we prove
Nikolskii--Besov regularity of a polynomial image of a Skorohod differentiable
measure on $\mathbb{R}^n$.
