POROSITY IN THE SPACE OF HÖLDER-FUNCTIONS

Mohammed Bachir (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

Let (X, d) be a bounded metric space with a base point 0 X , (Y, •) be a Banach space and Lip α 0 (X, Y) be the space of all α-Hölderfunctions that vanish at 0 X , equipped with its natural norm (0 < α ≤ 1). Let 0 < α < β ≤ 1. We prove that Lip β 0 (X, Y) is a σ-porous subset of Lip α 0 (X, Y), if (and only if) inf{d(x, x ′) : x, x ′ ∈ X; x = x ′ } = 0 (i.e. d is non-uniformly discrete). A more general result will be given.

Mots clés: 47L05; 46B25; 2010 Mathematics Subject Classification: 26A16; 54E52

Domaines: Analyse fonctionnelle [math.FA]

Mohammed Bachir. POROSITY IN THE SPACE OF HÖLDER-FUNCTIONS. 2021. ⟨hal-03222485v2⟩