# On fractional regularity of distributions of functions in Gaussian random variables

## TL;DR

This paper investigates the fractional smoothness of measures derived from Gaussian distributions through Sobolev class mappings, establishing fractional regularity results under weak nondegeneracy conditions.

## Contribution

It introduces new results on the fractional regularity of Gaussian measure images, extending understanding of their smoothness properties under weak assumptions.

## Key findings

- Established Nikolskii--Besov fractional regularity for Gaussian measure images.
- Derived fractional smoothness results under weak nondegeneracy conditions.
- Extended the theory of measure regularity in Gaussian spaces.

## Abstract

We study fractional smoothness of measures on $\mathbb{R}^k$, that are images of a Gaussian measure under mappings from Gaussian Sobolev classes. As a consequence we obtain Nikolskii--Besov fractional regularity of these distributions under some weak nondegeneracy assumption.