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arXiv · 2505.07788

A counterexample for local smoothing for averages over curves

David Beltran·Jonathan Hickman
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Abstract

We provide a new necessary condition for local smoothing estimates for the averaging operator defined by convolution with a measure supported on a smooth non-degenerate curve in $\mathbb{R}^n$ for $n \geq 3$. This demonstrates a limitation in the strength of local smoothing estimates towards establishing bounds for the corresponding maximal functions when $n \geq 5$.

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David Beltran, Jonathan Hickman. 2025-05-12. A counterexample for local smoothing for averages over curves. https://arxiv.org/abs/2505.07788

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