J. Bastero

activity

19922016

collaborators

8 papers

math.FA2016

The variance conjecture on hyperplane projections of l_p^n balls

David Alonso-Gutiérrez, Jesús Bastero

We show that for any $1 \leq p \leq \infty$ , the family of random vectors uniformly distributed on hyperplane projections of the unit ball of $ℓ_{p}^{n}$ verify the variance conjecture…

math.FA2012

The variance conjecture on some polytopes

David Alonso-Gutiérrez, Jesús Bastero

We show that any random vector uniformly distributed on any hyperplane projection of $B_{1}^{n}$ or $B_{\infty}^{n}$ verifies the variance conjecture $$\text{Var}|X|^2\leq C\sup_{ξ\in S^{n…

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.

math.FA2000

Inequalities for the Gamma Function and estimates for the volume of sections of $B_{p}^{n}$

Jesus Bastero, Fernando Galve, Ana Pena +1

We consider $k$ -dimensional central sections of the unit ball of $ℓ_{p}^{n}$ (denoted $B_{p}^{n}$ ) and we prove that their volume are bounded by the volume of $B_{p}^{n}$ whenever $1 < p < 2$ a…

math.FA1995

An extension of Milman's reverse Brunn-Minkowski inequality

Jesus Bastero, J. Bernues, A. Pena

The classical Brunn-Minkowski inequality states that for $A_{1}, A_{2} \subset R^{n}$ compact, $$ |A_1+A_2|^{1/n}\ge |A_1|^{1/n}+|A_2|^{1/n}\eqno(1) $$ where $∣ \cdot ∣$ denotes the Lebesgue…