On discrete Borell–Brascamp–Lieb inequalities

  1. David Iglesias
  2. Jesús Yepes Nicolás 1
  1. 1 Universidad de Murcia
    info

    Universidad de Murcia

    Murcia, España

    ROR https://ror.org/03p3aeb86

Revista:
Revista matemática iberoamericana

ISSN: 0213-2230

Año de publicación: 2020

Volumen: 36

Número: 3

Páginas: 711-722

Tipo: Artículo

DOI: 10.4171/RMI/1145 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Revista matemática iberoamericana

Resumen

If f,g,h:Rn⟶R≥0 are non-negative measurable functions such that h(x+y) is greater than or equal to the p-sum of f(x) and g(y), where −1/n≤p≤∞, p≠0, then the Borell–Brascamp–Lieb inequality asserts that the integral of h is not smaller than the q-sum of the integrals of f and g, for q=p/(np+1). In this paper we obtain a discrete analog for the sum over finite subsets of the integer lattice Zn: under the same assumption as before, for A,B⊂Zn}, then ∑A+Bh≥[(∑rf(A)f)q+(∑Bg)q]1/q, where rf(A) is obtained by removing points from A in a particular way, and depending on f. We also prove that the classical Borell–Brascamp–Lieb inequality for Riemann integrable functions can be obtained as a consequence of this new discrete version.

Fuente de los datos: Dialnet