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arXiv · 1005.1492

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

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

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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Jorge J. Betancor, Juan C. Fariña, Lourdes Rodríguez-Mesa, Ricardo Testoni. 2010-05-10. Higher order Riesz transforms in the ultraspherical setting as principal value integral operators. https://arxiv.org/abs/1005.1492

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