On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup

• Autores: Iris A. López P.
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 19, Nº. 2, 2017, págs. 11-31
• Idioma: inglés
• DOI: 10.4067/S0719-06462017000200011
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• Resumen
  • español

    Resumen: El objetivo de este artículo es demostrar la propiedad hipercontractiva del semigrupo de Dunkl-Ornstein-Uhlenbeck, .. Para lograr esto, probamos que el operador diferencial de Dunkl-Ornstein-Uhlenbeck Lk con k ≥ 0 y asociado al grupo , satisface una desigualdad de curvatura-dimensión, para ser precisos, una C(ρ,∞)-desigualdad, con 0≤ρ≤1. Como una aplicación de este hecho, obtenemos una versión del teorema de multiplicadores de Meyer y a través de este teorema y derivadas fraccionales, obtenemos una caracterización de espacios Dunkl-potenciales.

  • English

    Abstract: The aim of this paper is to prove the hypercontractive propertie of the Dunkl-Ornstein-Uhlenbeck semigroup, . To this end, we prove that the Dunkl-Ornstein-Uhlenbeck differential operator Lk with k ≥ 0 and associated to the 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.

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