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 diferential operator. We obtain explicit estimates of the $L^p$-norms for the Bessel-Riesz transforms in terms of p, establishing a linear behaviour 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.

References in corpus (6)

• Calderón-Zygmund operators in the Bessel setting
• Harmonic Analysis Operators Associated with Multidimensional Bessel Operators
• Dimension-free $L^p$ estimates for vectors of Riesz transforms associated with orthogonal expansions
• Dimension free $L^p$ estimates for Riesz transforms via an $H^{\infty }$ joint functional calculus
• Sharp dimension free bound for the Bakry-Riesz vector
• Linear dimension-free estimates for the Hermite-Riesz transforms