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L1-SMOOTHING FOR THE ORNSTEIN–UHLENBECK SEMIGROUP

  • K. Ball (a1), F. Barthe (a2), W. Bednorz (a3), K. Oleszkiewicz (a4) (a5) and P. Wolff (a6)...
Abstract
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.

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References
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[1]Beckner W., Inequalities in Fourier analysis. Ann. of Math. (2) 102(1) (1975), 159182.
[2]Bonami A., Etude des coefficients de Fourier des fonctions de L p(G). Ann. Inst. Fourier (Grenoble) 20(2) (1971), 335402.
[3]Nelson E., The free Markoff field. J. Funct. Anal. 12 (1973), 211227.
[4]Oleszkiewicz K., On Eaton’s property (in preparation).
[5]Talagrand M., A conjecture on convolution operators, and a non-Dunford–Pettis operator on L 1. Israel J. Math. 68(1) (1989), 8288.
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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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