On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup
- Iris A. López iathamaica@usb.ve
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DOI:
https://doi.org/10.4067/S0719-06462017000200011Abstract
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(Ï, ∞)-inequality, with 0 ≤ Ï â‰¤ 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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Published
2017-06-01
How to Cite
[1]
I. A. López, “On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup”, CUBO, vol. 19, no. 2, pp. 11–31, Jun. 2017.
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