Related papers: Finite bounds for Holder-Brascamp-Lieb multilinear…
In this paper, we establish a general weighted Hardy type inequality for the $% p-$Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results for different weights. Furthermore, we present…
The Brascamp-Lieb inequality in harmonic analysis was proved by Brascamp and Lieb in the rank one case in 1976, and by Lieb in 1990. It says that in a certain inequality, the optimal constant can be determined by checking the inequality for…
We give several new applications of our theorem on the existence of multiplicity of graded families of ideals as a limit, including a very general Minkowski type inequality for graded families of ideals, a very general formula for existence…
We give a criterion for bounding the homological finiteness length of certain HF-groups. This is used in two distinct contexts. Firstly, the homological finiteness length of a non-uniform lattice on a locally finite n-dimensional…
We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao.
We provide an alternative and self contained proof of the main result of Bennett, Carbery, Tao regarding the multilinear restriction estimate. The approach is inspired by the recent result of Guth about the Kakeya version of multilinear…
We give an explicit upper bound for the number of equivalence classes of binary forms with rational integral coefficients of given degree and given discriminant, and with given splitting field. Further, we give an explicit upper bound for…
The classical Loomis-Whitney inequality and the uniform cover inequality of Bollob\'{a}s and Thomason provide lower bounds for the volume of a compact set in terms of its lower dimensional coordinate projections. We provide further…
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent…
The Hardy--Littlewood inequalities for multilinear forms on sequence spaces state that for all positive integers $m,n\geq2$ and all $m$-linear forms $T:\ell_{p_{1}}^{n}\times\cdots\times\ell_{p_{m}}^{n}\rightarrow\mathbb{K}$…
We establish multilinear $L^p$ bounds for a class of maximal multilinear averages of functions on one variable, reproving and generalizing the bilinear maximal function bounds of Lacey. As an application we obtain almost everywhere…
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
The notion of multipolynomials was recently introduced and explored by T. Velanga in [10] as an attempt to encompass the theories of polynomials and multi- linear operators. In the present paper we push this subject further, by proving…
The goal of this overview article is to give a tangible presentation of recent breakthrough works in discrepancy theory by M. B. Levin. These works provide proofs for the exact lower discrepancy bounds of Halton's sequence and a certain…
We derive two concentration inequalities for linear functions of log-concave distributions: an enhanced version of the classical Brascamp--Lieb concentration inequality, and an inequality quantifying log-concavity of marginals in a manner…
Using elementary techniques, we prove sharp anisotropic Hardy-Littlewood inequalities for positive multilinear forms. In particular, we recover an inequality proved by F. Bayart in 2018.
We give a short proof of the Brascamp-Lieb theorem, which asserts that a certain general form of Young's convolution inequality is saturated by Gaussian functions. The argument is inspired by Borell's stochastic proof of the…
A new adaptive approach is proposed for variational inequalities with a Lipschitz-continuous field. Estimates of the necessary number of iterations are obtained to achieve a given quality of the variational inequality solution. A…
We give an overview of recent results on Lieb-Robinson bounds and some of their applications in the study of quantum many-body models in condensed matter physics.
Here a mixed problem for a nonlinear hyperbolic equation with Neumann boundary value condition is investigated, and a priori estimations for the possible solutions of the considered problem are obtained. These results demonstrate that any…