Related papers: Adjoint Brascamp-Lieb inequalities
Elementary proofs of sharp isoperimetric inequalities on a normed space $(\mathbb{R}^n,||\cdot||)$ equipped with a measure $\mu = w(x) dx$ so that $w^p$ is homogeneous are provided, along with a characterization of the corresponding…
B\"or\"oczky, Lutwak, Yang and Zhang recently proved the log-Brunn-Minkowski inequality which is stronger than the classical Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane. This paper establishes the…
We construct the upper and lower Bellman functions for the $L^p$ (quasi)-norms of BMO functions. These appear as solutions to a series of Monge--Amp\`ere boundary value problems on a non-convex plane domain. The knowledge of the Bellman…
In 1998, Bou\'e and Dupuis proved a variational representation for exponentials of bounded Wiener functionals. Since their proof involves arguments related to the weak convergence of probability measures, the boundedness of functionals…
Trace conjunction integrals are introduced and studied. They appear in trace conjunction inequalities which unify the Hardy inequality on a halfspace and the classical Gagliardo trace inequality. At the endpoint they satisfy a…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…
We establishe an affine Hardy-Littlewood-Sobolev inequality concerning two different functions which is stronger than the classical Hardy-Littlewood-Sobolev inequality. Furthermore, we also prove reverse inequalities for the new…
We review some topics in the theory of symmetric decreasing rearrangements with a particular focus on Lieb's fundamental contributions. Topics covered include the Brascamp--Lieb--Luttinger theorem, the sharp Young and…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…
This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity…
We study to what extent Lieb--Thirring inequalities are extendable from self-adjoint to general (possibly non-self-adjoint) Jacobi and Schr\"{o}dinger operators. Namely, we prove the conjecture of Hansmann and Katriel from [Complex Anal.…
The paper establishes a new family of sharp analytic inequalities. Together with the fractional Sobolev inequalities of Almgren and Lieb, they form a complete class of analytic inequalities, referred to as the chord Sobolev inequalities. A…
In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does…
The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is considered. Inequalities of the Wigner form are derived but shown to be extremely limiting in their applicability due to the nature of the…
We revisit an ingenious argument of K. Ball to provide sharp estimates for the volume of sections of a convex body in John's position. Our technique combines the geometric Brascamp-Lieb inequality with a generalised Parseval-type identity.…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function.…
We give a $L^2\times L^2 \rightarrow L^2$ convolution estimate for singular measures supported on transversal hypersurfaces in $\mathbb{R}^n$, which improves earlier results of Bejenaru, Herr & Tataru as well as Bejenaru & Herr. The arising…
In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequalities. In particular, we present \begin{align*}…
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number…
In this article, we study the further refinements and reverses of the Young and Heinz inequalities with the Kantorovich constant. These modified inequalities are used to establish corresponding operator inequalities on Hilbert space and…