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.
Distributions of polynomials in Gaussian random variables under structural constraints
On products of Gaussian random variables
Symmetric representations of distributions over $\mathbb{R}^2$ by distributions with not more than three-point supports
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