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A curved three-dimensional simplex Hilbert transform
Abstract
We prove Lebesgue space estimates for a curved three-dimensional simplex Hilbert transform associated with the moment curve t ↦ (t,t2,t3). 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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BibTeX
@misc{durcik2026curved,
title = {{A curved three-dimensional simplex Hilbert transform}},
author = {Polona Durcik and Marco Fraccaroli and Joris Roos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24850},
eprint = {2610.24850},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24850},
}
RIS
TY - UNPB
TI - A curved three-dimensional simplex Hilbert transform
AU - Polona Durcik
AU - Marco Fraccaroli
AU - Joris Roos
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24850
UR - https://arxiv.org/abs/2610.24850
AB - We prove Lebesgue space estimates for a curved three-dimensional simplex Hilbert transform associated with the moment curve t ↦ (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.
ER -