Bellman functions and dimension free [formula omitted]-estimates for the Riesz transforms in Bessel settings

Abstract

In this article we prove dimension free Lp–boundedness of Riesz transforms associated with a Bessel differential operator. We obtain explicit estimates of the Lp–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.