PreprintarXiv licencearXiv
Complex median method
Abstract
In this paper, we complete the characterization of the boundedness of higher order commutators of pointwise multiplication and a large class of singular integral operators, when the corresponding kernels satisfy certain non-degenerate conditions. This was known with the restriction that the pointwise multiplier is real-valued. We finally remove this restriction by proposing a novel complex median method. We also showcase the flexibility of this method by proving the necessity of the rectangular product BMO for the bi-commutators.
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BibTeX
@misc{li2026complex,
title = {{Complex median method}},
author = {Jinsong Li and Kangwei Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.28088},
eprint = {2609.28088},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28088},
}
RIS
TY - UNPB
TI - Complex median method
AU - Jinsong Li
AU - Kangwei Li
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.28088
UR - https://arxiv.org/abs/2609.28088
AB - In this paper, we complete the characterization of the boundedness of higher order commutators of pointwise multiplication and a large class of singular integral operators, when the corresponding kernels satisfy certain non-degenerate conditions. This was known with the restriction that the pointwise multiplier is real-valued. We finally remove this restriction by proposing a novel complex median method. We also showcase the flexibility of this method by proving the necessity of the rectangular product BMO for the bi-commutators.
ER -