## Bernoulli

• Bernoulli
• Volume 25, Number 4A (2019), 3090-3108.

### $\Phi$-entropy inequalities and asymmetric covariance estimates for convex measures

Van Hoang Nguyen

#### Abstract

In this paper, we use the semi-group method and an adaptation of the $L^{2}$-method of Hörmander to establish some $\Phi$-entropy inequalities and asymmetric covariance estimates for the strictly convex measures in $\mathbb{R}^{n}$. These inequalities extends the ones for the strictly log-concave measures to more general setting of convex measures. The $\Phi$-entropy inequalities are turned out to be sharp in the special case of Cauchy measures. Finally, we show that the similar inequalities for log-concave measures can be obtained from our results in the limiting case.

#### Article information

Source
Bernoulli, Volume 25, Number 4A (2019), 3090-3108.

Dates
Revised: September 2018
First available in Project Euclid: 13 September 2019

https://projecteuclid.org/euclid.bj/1568362053

Digital Object Identifier
doi:10.3150/18-BEJ1082

Mathematical Reviews number (MathSciNet)
MR4003575

Zentralblatt MATH identifier
07110122

#### Citation

Nguyen, Van Hoang. $\Phi$-entropy inequalities and asymmetric covariance estimates for convex measures. Bernoulli 25 (2019), no. 4A, 3090--3108. doi:10.3150/18-BEJ1082. https://projecteuclid.org/euclid.bj/1568362053

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