Fractional smoothness of images of logarithmically concave measures under polynomials
Probability
2016-05-03 v1
Abstract
We show that a measure on the real line that is the image of a log-concave measure under a polynomial of degree possesses a density from the Nikol'skii--Besov class of fractional order . This result is used to prove an estimate of the total variation distance between such measures in terms of the Fortet--Mourier distance.
Keywords
Cite
@article{arxiv.1605.00162,
title = {Fractional smoothness of images of logarithmically concave measures under polynomials},
author = {Egor D. Kosov},
journal= {arXiv preprint arXiv:1605.00162},
year = {2016}
}