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$\Phi-$entropy inequalities and asymmetric covariance estimates for convex measures. (arXiv:1810.07141v1 [math.FA])
来源于:arXiv
In this paper, we use the semi-group method and an adaptation of the
$L^2-$method of H\"ormander 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. 查看全文>>