Lp–dimension free boundedness for Riesz transforms associated to Hermite functions⋆
By E. Harboure, L. Rosa, C. Segovia, José L. Torrea. 2004
55 citations recorded by the source corpus.
Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on 1<p< ∞. In this paper we give a different proof that allows us to show that the Lp−norms of these operators are bounded by a constant not depending on the dimension d. Moreover, we define Riesz transforms of higher order and free dimensional estimates of the Lp−bounds of these operators are obtained. In order to prove the mentioned results we give an extension of the Littlewood-Paley theory that we believe of independent interest.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/9d010ef106621f192a37d6afc48a5f6217f7e66b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Javier Parcet
- Tao Mei
- Marius Junge
- Quanhua Xu
- Narcisse Randrianantoanina
- A. Gonz'alez-P'erez
- Sjoerd Dirksen
- Uffe Haagerup
Citations in the corpus
- Noncommutative Riesz transforms -- Dimension free bounds and Fourier multipliers (2014, background): “ature in Riemannian manifolds [4, 41]. Clifford algebras were considered by Lust-Piquard [44, 45] and other topics concerning Hermite or Laguerre processes and optimal linear estimates can be found in [11, 20, 27, 28] and the references therein. Further dimension free estimates for maximal functions ”
- Extension Problem and Harnack's Inequality for Some Fractional Operators (2009, unknown): “2) and the fact that (see [5]) e−tH1 x = 1 cosh 2t n/2 e− tanh 2t 2 x 2 ≤ 1 (5.”