The aim of this paper is to prove the hypercontractive propertie of the Dunkl-Ornstein-Uhlenbeck semigroup, {e(tLk)}t≥0. To this end, we prove that the Dunkl-Ornstein-Uhlenbeck differential operator Lk with k ≥ 0 and associated to the ℤd2 group, satisfies a curvature-dimension inequality, to be precise, a C(ρ, ∞)-inequality, with 0 ≤ ρ ≤ 1. As an application of this fact, we get a version of Meyer’s multipliers theorem and by means of this theorem and fractional derivatives, we obtain a characterization of Dunkl-potential spaces.
@article{1576,
title = {On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup},
journal = {CUBO, A Mathematical Journal},
volume = {19},
year = {2017},
language = {en},
url = {http://dml.mathdoc.fr/item/1576}
}
L´opez, Iris A. On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup. CUBO, A Mathematical Journal, Tome 19 (2017) . http://gdmltest.u-ga.fr/item/1576/