# Regularity of linear and polynomial images of Skorohod differentiable measures

## TL;DR

This paper investigates the regularity properties of linear and polynomial transformations of Skorohod differentiable measures, providing estimates and regularity results that advance understanding of their structure and behavior.

## Contribution

It introduces new estimates for the Skorohod derivative norm of projections and establishes Nikolskii--Besov regularity for polynomial images of these measures.

## Key findings

- Derived bounds for the Skorohod derivative norm of measure projections
- Proved Nikolskii--Besov regularity for polynomial images of Skorohod differentiable measures
- Enhanced understanding of the regularity properties of measure transformations

## Abstract

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 $\mathbb{R}^n$.