Higher order Riesz transforms in the ultraspherical setting as principal value integral operators

Jorge J. Betancor, Juan C. Fariña, Lourdes Rodríguez-Mesa, Ricardo Testoni

Published 2010-05-10Version 1

In this paper we represent the $k$-th Riesz transform in the ultraspherical setting as a principal value integral operator for every $k\in \mathbb{N}$. We also measure the speed of convergence of the limit by proving $L^p$-boundedness properties for the oscillation and variation operators associated with the corresponding truncated operators.