Asymmetric Covariance Estimates of Brascamp-Lieb Type and Related Inequalities for Log-concave Measures

Details Asymmetric Covariance Estimates of Brascamp-Lieb Type and Related Inequalities for Log-concave Measures Asymmetric Covariance Estimates of Brascamp-Lieb Type and Related Inequalities for Log-concave Measures

2011-06-03

arxiv.org/abs/1106.0709v2

Mathematics

Functional Analysis

16 pages. This version corrects some misprints, and contains additional comments on the results

Scientific paper

An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the $L^2$ norms of the gradients of the functions, where the magnitude of the gradient is computed using an inner product given by the inverse Hessian matrix of the potential of the log-concave measure. Menz and Otto \cite{OM} proved a variant of this with the two $L^2$ norms replaced by $L^1$ and $L^\infty$ norms, but only for $\R^1$. We prove a generalization of both by extending these inequalities to $L^p$ and $L^q$ norms and on $\R^n$, for any $n\geq 1$. We also prove an inequality for integrals of divided differences of functions in terms of integrals of their gradients.

Affiliated with

Also associated with

No associations

Rating

Asymmetric Covariance Estimates of Brascamp-Lieb Type and Related Inequalities for Log-concave Measures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymmetric Covariance Estimates of Brascamp-Lieb Type and Related Inequalities for Log-concave Measures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymmetric Covariance Estimates of Brascamp-Lieb Type and Related Inequalities for Log-concave Measures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-224219