Mathematika

Research Article

L 1-SMOOTHING FOR THE ORNSTEIN–UHLENBECK SEMIGROUP

K. Balla1, F. Barthea2, W. Bednorza3, K. Oleszkiewicza4a5 and P. Wolffa6

a1 Mathematics Institute, University of Warwick, Coventry, CV4 7AL, U.K. (email: kmb120205@googlemail.com)

a2 Institut de Mathématiques de Toulouse (CNRS UMR 5219), Université Paul Sabatier, 31062 Toulouse cedex 09, France (email: barthe@math.univ-toulouse.fr)

a3 Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland (email: W.Bednorz@mimuw.edu.pl)

a4 Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

a5 Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland (email: K.Oleszkiewicz@mimuw.edu.pl)

a6 Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland (email: pwolff@mimuw.edu.pl)

Abstract

Given a probability density, we estimate the rate of decay of the measure of the level sets of its evolutes by the Ornstein–Uhlenbeck semigroup. The rate is faster than what follows from the preservation of mass and Markov’s inequality.

(Online publication August 02 2012)

MSC (2010)

  • 46N30;
  • 60E15 (primary)

Footnotes

The research of the third, fourth and fifth authors was partially supported by the Polish MNiSzW grants 1 PO3A 012 29 and N N201 397437.