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arXiv · 2501.00858

Maximal estimates for averages over degenerate hypersurfaces

Sewook Oh
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Abstract

We study $L^p$ boundedness of the maximal average over dilations of a smooth hypersurface $S$. When the decay rate of the Fourier transform of a measure on $S$ is $1/2$, we establish the optimal maximal bound, which settles the conjecture raised by Stein. Additionally, when $S$ is not flat, we verify that the maximal average is bounded on $L^p$ for some finite $p$, which generalizes the result by Sogge and Stein.

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Sewook Oh. 2025-01-01. Maximal estimates for averages over degenerate hypersurfaces. https://arxiv.org/abs/2501.00858

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