Bellman functions and dimension free L p -estimates for the Riesz transforms in Bessel settings

Abstract

In this article we prove dimension free $L^p$?boundedness of Riesz transforms associated with a Bessel differential operator. We obtain explicit estimates of the $L^p$?norms for the Bessel?Riesz transforms in terms of $p$, establishing a linear behavior with respect to $p$. We use the Bellman function technique to prove a bilinear dimension free inequality involving Poisson semigroups defined through this Bessel operator.