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Higher Order Riesz Transforms in the Ultraspherical Setting as Principal Value Integral Operators |
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| Authors: | Jorge J. Betancor Juan C. Fariña Lourdes Rodríguez-Mesa Ricardo Testoni |
| Affiliation: | 1.Departamento de Análisis Matemático,Universidad de la Laguna,La Laguna (Sta. Cruz de Tenerife),Spain;2.Departamento de Matemática,Universidad Nacional del Sur,Bahía Blanca, Buenos Aires,Argentina |
| Abstract: | In this paper we represent the kth 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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