Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy--Landau--Littlewood inequality

Vladimir I. Bogachev, Egor D. Kosov, Georgii I. Zelenov

We prove that the distribution density of any non-constant polynomial $f({\xi }_1,{\xi }_2,\dots )$ of degree $d$ in independent standard Gaussian random variables $\xi$ (possibly, in infinite…