PreprintCC BY 4.0arXiv
Best constants in noncommutative Burkholder inequalities
Abstract
The paper contains the study of noncommutative Burkholder inequalities. We prove that the constant involved is of order O(p/log p) when p→ ∞, which is known to be optimal even in the commutative setting. This answers an open problem raised by Randrianantoanina in 2007, and by Junge and Xu in 2008.
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BibTeX
@misc{jiao2026best,
title = {{Best constants in noncommutative Burkholder inequalities}},
author = {Yong Jiao and Adam Osekowski and Lian Wu and Yahui Zuo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30600},
eprint = {2609.30600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30600},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Best constants in noncommutative Burkholder inequalities
AU - Yong Jiao
AU - Adam Osekowski
AU - Lian Wu
AU - Yahui Zuo
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30600
UR - https://arxiv.org/abs/2609.30600
AB - The paper contains the study of noncommutative Burkholder inequalities. We prove that the constant involved is of order O(p/log p) when p→ ∞, which is known to be optimal even in the commutative setting. This answers an open problem raised by Randrianantoanina in 2007, and by Junge and Xu in 2008.
ER -