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arXiv · 1505.00229

Remarks on the maximal operator and Hilbert transform along variable parabolas

Shaoming Guo
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Abstract

We prove the boundedness of the maximal operator and Hilbert transform along certain variable parabolas in $L^p$ for $p>p_0$ with some $p_0\in (1, 2)$. Connections with the Hilbert transform along vector fields and the polynomial Carleson's maximal operator are also discussed.

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Shaoming Guo. 2015-05-01. Remarks on the maximal operator and Hilbert transform along variable parabolas. https://arxiv.org/abs/1505.00229

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