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

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

2010-05-10

arxiv.org/abs/1005.1492v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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