Related papers: Reverse Brascamp-Lieb inequality and the dual Boll…

We present a regularized version of H\"{o}lder-Brascamp-Lieb inequalities studied by Bennett, Carbery, Christ, and Tao. These inequalities lead to a generalization of the multilinear Kakeya inequality.

We prove a sharp common generalization of endpoint multilinear Kakeya and local discrete Brascamp-Lieb inequalities.

We give a new proof of the sharp form of Young's inequality for convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BL]. The latter also proved a sharp reverse inequality in the case of exponents less than $1$. Our proof is…

We adapt an induction-on-scales argument of Bennett, Bez, Buschenhenke, Cowling, and Flock to establish a global near-monotonicity statement for the nonlinear Brascamp-Lieb functional under a certain heat-flow, from which follows a…

Some additive reverses of the generalised triangle inequality in normed linear spaces are given. Applications for complex numbers are provided as well.

The purpose of this paper is to provide a random version of Simons' inequality.

We consider the Brascamp--Lieb inequalities concerning multilinear integrals of products of functions in several dimensions. We give a complete treatment of the issues of finiteness of the constant, and of the existence and uniqueness of…

We prove an $L^2$-stability estimate for the variance Brascamp-Lieb inequality [J. Funct. Anal. 22 (4), 366-389 (1976)] by bootstrapping the recent $L^1$-stability theorem of Machado and Ramos [arXiv:2511.22636] under an additional…

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

In this short note we would like to show that one can use Davies's Hardy inequality to rederive well-known results of Lieb and Rozenblum.

We propose algebraic criteria that yield sharp H\"{o}lder types of inequalities for the product of functions of Gaussian random vectors with arbitrary covariance structure. While our lower inequality appears to be new, we prove that the…

In this paper, we study new extensions of the functional Blaschke-Santalo inequalities, and explore applications of such new inequalities beyond the classical setting of the standard Gaussian measure.

We strengthen the volume inequalities for L_p zonoids of even isotropic measures and for their duals, which are due to Ball, Barthe and Lutwak, Yang, Zhang. Along the way, we prove a stronger version of the Brascamp-Lieb inequality for a…

Certain rearrangement inequalities of a type considered by Hardy, Riesz, and Brascamp-Lieb-Luttinger are studied. Subsets of the real line that extremize these inequalities are characterized. Our results apply only to special cases, and…

We prove an inequality on positive real numbers, that looks like a reverse to the well-known Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal.

We provide a new characterization of the logarithmic Sobolev inequality.

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…

The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…

We strengthen, in two different ways, the so called Borell-Brascamp- Lieb inequality in the class of power concave functions with compact support. As examples of applications we obtain two quantitative versions of the Brunn- Minkowski…

In this paper we survey wqo and bqo theory from the reverse mathematics perspective. We consider both elementary results (such as the equivalence of different definitions of the concepts, and basic closure properties) and more advanced…