Inequalities for second-order Riesz transforms associated with Bessel expansions

Volume 68 / 2020

Adam Osękowski Bulletin Polish Acad. Sci. Math. 68 (2020), 75-88 MSC: Primary 42B15, 42B20; Secondary 42B10, 60G44. DOI: 10.4064/ba200302-5-10 Published online: 15 October 2020

Abstract

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.

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