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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oai:scielo:S0719-064620170002000112018-04-25On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroupLópez,Iris A. Dunkl-Ornstein-Uhlenbeck operator generalized Hermite polynomial squared field operator Meyer's multiplier theorem Dunkl-potential space fractional integral fractional derivative. 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.19 n.2 20172017-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462017000200011en10.4067/S0719-06462017000200011 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Dunkl-Ornstein-Uhlenbeck operator generalized Hermite polynomial squared field operator Meyer's multiplier theorem Dunkl-potential space fractional integral fractional derivative. |
| spellingShingle |
Dunkl-Ornstein-Uhlenbeck operator generalized Hermite polynomial squared field operator Meyer's multiplier theorem Dunkl-potential space fractional integral fractional derivative. López,Iris A. On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup |
| description |
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. |
| author |
López,Iris A. |
| author_facet |
López,Iris A. |
| author_sort |
López,Iris A. |
| title |
On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup |
| title_short |
On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup |
| title_full |
On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup |
| title_fullStr |
On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup |
| title_full_unstemmed |
On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup |
| title_sort |
on the hypercontractive property of the dunkl-ornstein-uhlenbeck semigroup |
| publisher |
Universidad de La Frontera. Departamento de Matemática y Estadística. |
| publishDate |
2017 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462017000200011 |
| work_keys_str_mv |
AT lopezirisa onthehypercontractivepropertyofthedunklornsteinuhlenbecksemigroup |
| _version_ |
1714206796753666048 |