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arXiv · 2305.16221

The elliptic maximal function

Juyoung Lee·Sanghyuk Lee·Sewook Oh
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Abstract

We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq \infty$. For this purpose, we obtain some sharp multi-parameter local smoothing estimates.

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Juyoung Lee, Sanghyuk Lee, Sewook Oh. 2023-05-25. The elliptic maximal function. https://arxiv.org/abs/2305.16221

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