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The Cp conjecture of Muckenhoupt
Abstract
We give an affirmative answer to Muckenhoupt's Cp conjecture: for 1<p<∞, the Cp condition is necessary and sufficient for the weighted Lp(w) norm inequality relating the Hilbert transform and the Hardy--Littlewood maximal operator. We also show that the Cp condition is necessary and sufficient for the weighted Fefferman--Stein inequality.
Related
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BibTeX
@misc{lerner2026conjecture,
title = {{The $C_p$ conjecture of Muckenhoupt}},
author = {Andrei K. Lerner and Sheldy Ombrosi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34099},
eprint = {2610.34099},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34099},
}
RIS
TY - UNPB
TI - The C_p conjecture of Muckenhoupt
AU - Andrei K. Lerner
AU - Sheldy Ombrosi
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34099
UR - https://arxiv.org/abs/2610.34099
AB - We give an affirmative answer to Muckenhoupt's C_p conjecture: for 1<p<∞, the C_p condition is necessary and sufficient for the weighted L^p(w) norm inequality relating the Hilbert transform and the Hardy--Littlewood maximal operator. We also show that the C_p condition is necessary and sufficient for the weighted Fefferman--Stein inequality.
ER -