English

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

Classical Analysis and ODEs 2010-05-11 v1

Abstract

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

Keywords

Cite

@article{arxiv.1005.1492,
  title  = {Higher order Riesz transforms in the ultraspherical setting as principal value integral operators},
  author = {Jorge J. Betancor and Juan C. Fariña and Lourdes Rodríguez-Mesa and Ricardo Testoni},
  journal= {arXiv preprint arXiv:1005.1492},
  year   = {2010}
}
R2 v1 2026-06-21T15:20:28.609Z