PreprintCC BY 4.0arXiv
Boundedness of Multilinear Hilbert Transforms Along Moment Curves
Abstract
We prove the boundedness of multilinear Hilbert transforms along moment curves by establishing uniform estimates for both translated and untranslated multilinear paraproducts and by applying a Sobolev smoothing inequality. As a byproduct of our method, we obtain the same bounds for multilinear maximal functions along moment curves.
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BibTeX
@misc{guo2026boundedness,
title = {{Boundedness of Multilinear Hilbert Transforms Along Moment Curves}},
author = {Jingwei Guo and Xiaochun Li and Guoqing Zhan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07513},
eprint = {2609.07513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07513},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Boundedness of Multilinear Hilbert Transforms Along Moment Curves
AU - Jingwei Guo
AU - Xiaochun Li
AU - Guoqing Zhan
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.07513
UR - https://arxiv.org/abs/2609.07513
AB - We prove the boundedness of multilinear Hilbert transforms along moment curves by establishing uniform estimates for both translated and untranslated multilinear paraproducts and by applying a Sobolev smoothing inequality. As a byproduct of our method, we obtain the same bounds for multilinear maximal functions along moment curves.
ER -