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On the matrix Ap conjecture
Abstract
This paper provides a solution to the matrix Ap conjecture. For every 1<p<∞, we construct a family of 2×2 matrix Ap weights W with arbitrarily large characteristics for which |H|Lp(W)→ Lp(W)≥ cp[W]Ap1+1/[p(p−1)], where H is the Hilbert transform and cp>0 depends only on p.
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BibTeX
@misc{jiao2026matrix,
title = {{On the matrix $A_p$ conjecture}},
author = {Yong Jiao and Xingyan Quan and Lian Wu and Guangheng Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.14584},
eprint = {2609.14584},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14584},
}
RIS
TY - UNPB
TI - On the matrix A_p conjecture
AU - Yong Jiao
AU - Xingyan Quan
AU - Lian Wu
AU - Guangheng Xie
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2609.14584
UR - https://arxiv.org/abs/2609.14584
AB - This paper provides a solution to the matrix A_p conjecture. For every 1<p<∞, we construct a family of 2×2 matrix A_p weights W with arbitrarily large characteristics for which |H|_L^p(W)→ L^p(W)≥ c_p[W]_A_p^1+1/[p(p−1)], where H is the Hilbert transform and c_p>0 depends only on p.
ER -