English

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 dd possesses a density from the Nikol'skii--Besov class of fractional order 1/d1/d. 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}
}