Julio Bernu'es

activity

20092020

collaborators

8 papers

math.FA2020

On affine invariant and local Loomis-Whitney type inequalities

David Alonso-Gutiérrez, Julio Bernués, Silouanos Brazitikos +1

We prove various extensions of the Loomis-Whitney inequality and its dual, where the subspaces on which the projections (or sections) are considered are either spanned by vectors $…

math.FA2019

An extension of Berwald's inequality and its relation to Zhang's inequality

David Alonso-Gutiérrez, Julio Bernués, Bernardo González Merino

In this note prove the following Berwald-type inequality, showing that for any integrable log-concave function $f : R^{n} \to [0, \infty)$ and any concave function $h:L\ri…

math.HO2019

Soñando con números, María Andresa Casamayor (1720-1780)

Julio Bernués, Pedro J. Miana

María Andresa Casamayor de la Coma, born in Zaragoza, is known as the first woman who published a scientific book in Spain. In this paper we provide answers to several of the most…

math.FA2018

Zhang's inequality for log-concave functions

David Alonso-Gutiérrez, Julio Bernués, Bernardo González Merino

Zhang's reverse affine isoperimetric inequality states that among all convex bodies $K \subseteq R^{n}$ , the affine invariant quantity $∣ K ∣^{n - 1} ∣ Π^{*} (K) ∣$ (where $Π^{*} (K)$ deno…

math.MG2018

The square negative correlation on l_p^n balls

David Alonso-Gutiérrez, Julio Bernués

In this paper we prove that for any $p \in [2, \infty)$ the $ℓ_{p}^{n}$ unit ball, $B_{p}^{n}$ , satisfies the square negative correlation property with respect to every orthonormal basis,…

math.FA2017

The variance conjecture on projections of the cube

David Alonso-Gutiérrez, Julio Bernués

We prove that the uniform probability measure $μ$ on every $(n - k)$ -dimensional projection of the $n$ -dimensional unit cube verifies the variance conjecture with an absolute constan…

math.FA2011

Factoring Sobolev inequalities through classes of functions

David Alonso-Gutiérrez, Jesús Bastero, Julio Bernués

We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools…

math.FA2009

On the isotropy constant of projections of polytopes

David Alonso-Gutiérrez, Jesús Bastero, Julio Bernués +1

The isotropy constant of any $d$ -dimensional polytope with $n$ vertices is bounded by $C n / d$ where $C > 0$ is a numerical constant.