3 papers
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 or 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 -dimensional polytope with vertices is bounded by where is a numerical constant.