On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup
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...
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| Lenguaje: | English |
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Universidad de La Frontera. Departamento de Matemática y Estadística.
2017
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| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462017000200011 |
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| Sumario: | 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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