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Regular version of the site

Article

Fractional smoothness of images of logarithmically concave measures under polynomials

Journal of Mathematical Analysis and Applications. 2018. Vol. 462. No. 1. P. 390-406.

We show that a measure on the real line, that is the image of a log-concave measure under a polynomial of degree d, possesses a density from the Nikolskii–Besov class of fractional order 1/d. This result is used to prove an estimate for the total variation distance between such measures in terms of the Fortet–Mourier distance.