Related papers: Effective Brascamp-Lieb inequalities

Recent progress in multilinear harmonic analysis naturally raises questions about the local behaviour of the best constant (or bound) in the general Brascamp--Lieb inequality as a function of the underlying linear transformations. In this…

We prove that the best constant in the general Brascamp-Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and nonlinear…

We establish a structure theorem for the Brascamp--Lieb constant formulated in the general setting of locally compact abelian groups. This extends and unifies the finiteness characterisations previously known for euclidean spaces and for…

We prove a nonlinear variant of the general Brascamp-Lieb inequality. Instances of this inequality are quite prevalent in analysis, and we illustrate this with substantial applications in harmonic analysis and partial differential…

We propose a new, self-contained, approach to H. Raufi's extension of Prekopa's theorem for matrix-valued log-concave functions. Along the way, new related inequalities are established, in particular a Brascamp-Lieb variance inequality for…

The optimal constants are found for Lebesgue norm multilinear inequalities of Holder-Brascamp-Lieb type for arbitrary discrete Abelian groups. Previously a criterion for finiteness of the constants had been established for finitely…

We reveal a connection of the Brascamp-Lieb inequality with Skorokhod embedding. Error bounds for the inequality in terms of variance are also provided.

We establish a nonlinear generalisation of the classical Brascamp-Lieb inequality in the case where the Lebesgue exponents lie in the interior of the finiteness polytope. As a corollary we show that the best constant in Young's convolution…

We consider a class of Brascamp-Lieb forms and give conditions which guarantee the boundedness of these form on $L^p$-spaces with weights that are a power of the distance to the origin. These conditions are close to necessary and…

We prove a reverse form of the multidimensional Brascamp-Lieb inequality. Our method also gives a new way to derive the Brascamp-Lieb inequality and is rather convenient for the study of equality cases.

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 formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings.

Brascamp-Lieb inequalities have been important in analysis, mathematical physics and neighboring areas. Recently, these inequalities have had a deep influence on Fourier analysis and, in particular, on Fourier restriction theory. In this…

We study stability issues for the so-called Borell-Brascamp-Lieb inequalities, proving that when near equality is realized, the involved functions must be $L^1$-close to be $p$-concave and to coincide up to homotheties of their graphs.

We prove a global nonlinear Brascamp-Lieb inequality for a general class of maps, encompassing polynomial and rational maps, as a consequence of the multilinear Kakeya-type inequalities of Zhang and Zorin-Kranich. We incorporate a natural…

We use Brascamp-Lieb's inequality to obtain new decoupling inequalities for general Gaussian vectors, and for stationary cyclic Gaussian processes. In the second case, we use a version by Bump and Diaconis of the strong Szego limit theorem.…

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

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…

By employing the recently obtained sharp stability versions of the Pr\'ekopa--Leindler inequality, we are able to obtain a sharp quantitative stability version for the Brascamp--Lieb inequality, as well as several different results on the…

H\"older-Brascamp-Lieb inequalities provide upper bounds for a class of multilinear expressions, in terms of $L^p$ norms of the functions involved. They have been extensively studied for functions defined on Euclidean spaces.…