Regularity of linear and polynomial images of Skorohod differentiable measures

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 $\mathbb{R}^n$.