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Curved commutators in higher dimensions
Abstract
We complete the characterization of the Lp boundedness of the commutators [b, Hγ] of pointwise multiplication and the Hilbert transform along monomial curves in any dimension. This fully solve a key point left open by Bongers, Guo, Li and Wick, which was affirmatively answered recently only for dimension two. We achieve this by a novel but elementary argument, avoiding the complicated geometry structure in higher dimensions.
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BibTeX
@misc{li2026curved,
title = {{Curved commutators in higher dimensions}},
author = {Kangwei Li and Yunan Zeng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18613},
eprint = {2609.18613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18613},
}
RIS
TY - UNPB
TI - Curved commutators in higher dimensions
AU - Kangwei Li
AU - Yunan Zeng
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18613
UR - https://arxiv.org/abs/2609.18613
AB - We complete the characterization of the L^p boundedness of the commutators [b, H_γ] of pointwise multiplication and the Hilbert transform along monomial curves in any dimension. This fully solve a key point left open by Bongers, Guo, Li and Wick, which was affirmatively answered recently only for dimension two. We achieve this by a novel but elementary argument, avoiding the complicated geometry structure in higher dimensions.
ER -