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Higher Order Riesz Transforms in the Ultraspherical Setting as Principal Value Integral Operators

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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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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271, La Laguna (Sta. Cruz de Tenerife), Spain

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

  2. Departamento de Matemática, Universidad Nacional del Sur, Avda. Alem 1253-2 Piso, 8000, Bahía Blanca, Buenos Aires, Argentina

    Ricardo Testoni

Authors
  1. Jorge J. Betancor
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  2. Juan C. Fariña
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  3. Lourdes Rodríguez-Mesa
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  4. Ricardo Testoni
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Corresponding author

Correspondence to Lourdes Rodríguez-Mesa.

Additional information

This paper is partially supported by MTM2010/17974.

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Betancor, J.J., Fariña, J.C., Rodríguez-Mesa, L. et al. Higher Order Riesz Transforms in the Ultraspherical Setting as Principal Value Integral Operators. Integr. Equ. Oper. Theory 70, 511–539 (2011). https://doi.org/10.1007/s00020-011-1880-5

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  • DOI: https://doi.org/10.1007/s00020-011-1880-5

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