发表机构
Nanjing Normal University; University of California, Irvine（南京师范大学; 加州大学尔湾分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究魏斯勒猜想中复超压缩性刻画在特定范围未解决的问题，通过证明相应两点不等式解决其余严格非对角情形，还证明了对特定\(p,q\)范围的两点不等式。
AI 中文摘要
魏斯勒关于汉明立方体上复超压缩性的猜想刻画在\(2 < p \leq q < 3\)和\(\frac{3}{2} < p \leq q < 2\)范围内仍未解决。伊万尼斯维利 - 纳扎罗夫证明了对角情形。我们通过相应的两点不等式证明了其余严格非对角情形。实际上，我们的论证证明了对每个\(2 < p < q < \infty\)的两点不等式，通过对偶性，对每个\(1 < p < q < 2\)也成立。
英文摘要
Weissler's conjectured characterization of complex hypercontractivity on the Hamming cube remained open in the ranges $2<p\le q<3$ and $\frac32<p\le q<2$. 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 $2<p\le q<\infty$ and, by duality, for every $1<p\le q<2$, including the previously known diagonal cases. The proof is based on a flow argument.
