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arXiv · 2610.24850

A curved three-dimensional simplex Hilbert transform

Polona Durcik·Marco Fraccaroli·Joris Roos
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Abstract

We prove Lebesgue space estimates for a curved three-dimensional simplex Hilbert transform associated with the moment curve $t \mapsto (t,t^2,t^3)$. The analysis relies on smoothing inequalities for curved multilinear averages and on estimates for a three-dimensional anisotropic variant of the twisted paraproduct. The result has been formally verified in Lean 4.

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Polona Durcik, Marco Fraccaroli, Joris Roos. 2026-10-17. A curved three-dimensional simplex Hilbert transform. https://arxiv.org/abs/2610.24850

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