Inequalities for second-order Riesz transforms associated with Bessel expansions

The paper contains the proofs of $L^p$, logarithmic and weak-type estimates for the second-order Riesz transforms arising in the context of multidimensional Bessel expansions. Using a novel probabilistic approach, which rests on martingale methods and the representation of Riesz transforms via associated Bessel-heat processes, we show that these estimates hold with constants independent of the dimension.