L p − dimension free boundedness for Riesz transforms associated to Hermite functions ∗

@inproceedings{Harboure2003LP,
  title={L p − dimension free boundedness for Riesz transforms associated to Hermite functions ∗},
  author={E. Harboure and L. De Rosa and Carlos Segovia and Jos{\'e} L. Torrea},
  year={2003}
}
Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on Lp(IRd), 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… CONTINUE READING