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arXiv · 2407.07563

On a planar Pierce--Yung operator

David Beltran·Shaoming Guo·Jonathan Hickman
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Abstract

We show that the operator \begin{equation*} \mathcal{C} f(x,y) := \sup_{v\in \mathbb{R}} \Big|\mathrm{p.v.} \int_{\mathbb{R}} f(x-t, y-t^2) e^{i v t^3} \frac{\mathrm{d} t}{t} \Big| \end{equation*} is bounded on $L^p(\mathbb{R}^2)$ for every $1 < p < \infty$. This gives an affirmative answer to a question of Pierce and Yung.

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David Beltran, Shaoming Guo, Jonathan Hickman. 2024-07-10. On a planar Pierce--Yung operator. https://arxiv.org/abs/2407.07563

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