Riesz potentials of Radon measures associated to reflection groups - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

Riesz potentials of Radon measures associated to reflection groups

Résumé

For a root system R on R d and a nonnegative multiplicity function k on R, we consider the heat kernel p k (t, x, y) associated to the Dunkl-Laplacian operator ∆ k. For β ∈]0, d + 2γ[, where γ = 1 2 ∑ α∈R k(α), we study the ∆ k-Riesz kernel of index β defined by R k,β (x, y) = 1 Γ(β/2) ∫ +∞ 0 t β 2 −1 p k (t, x, y)dt and the corresponding ∆ k-Riesz potential I k,β [µ] of a Radon measure µ on R d. According to the values of β, we study the ∆ k-superharmonicity of these functions and we give some applications like the ∆ k-Riesz measure of I k,β [µ], the uniqueness principle and a pointwise Hedberg's inequality.
Fichier principal
Vignette du fichier
GalRejSifi-Dunkl-Riesz Pot.pdf (175.38 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01451555 , version 1 (01-02-2017)

Identifiants

  • HAL Id : hal-01451555 , version 1

Citer

Léonard Gallardo, Chaabane Rejeb, Mohamed Sifi. Riesz potentials of Radon measures associated to reflection groups. 2017. ⟨hal-01451555⟩
221 Consultations
309 Téléchargements

Partager

Gmail Facebook X LinkedIn More