PreprintCC BY 4.0arXiv
The missing two-point inequality in Weissler's conjecture
Abstract
Weissler's conjectured characterization of complex hypercontractivity on the Hamming cube remained open in the ranges 2<p≤ q<3 and 3/2<p≤ q<2. Ivanisvili--Nazarov established the diagonal cases. We prove the remaining strict off-diagonal cases through the corresponding two-point inequality. Our argument gives a self-contained proof for every 2<p≤ q<∞ and, by duality, for every 1<p≤ q<2, including the previously known diagonal cases. The proof is based on a flow argument.
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BibTeX
@misc{huang2026missing,
title = {{The missing two-point inequality in Weissler's conjecture}},
author = {Yi C. Huang and Paata Ivanisvili},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.19769},
eprint = {2607.19769},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.19769},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The missing two-point inequality in Weissler's conjecture
AU - Yi C. Huang
AU - Paata Ivanisvili
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2607.19769
UR - https://arxiv.org/abs/2607.19769
AB - Weissler's conjectured characterization of complex hypercontractivity on the Hamming cube remained open in the ranges 2<p≤ q<3 and 3/2<p≤ q<2. Ivanisvili--Nazarov established the diagonal cases. We prove the remaining strict off-diagonal cases through the corresponding two-point inequality. Our argument gives a self-contained proof for every 2<p≤ q<∞ and, by duality, for every 1<p≤ q<2, including the previously known diagonal cases. The proof is based on a flow argument.
ER -