非交换尖锐Hausdorff-Young不等式
Noncommutative sharp Hausdorff-Young inequality
- Institute for Advanced Study in Mathematics, Harbin Institute of Technology（哈尔滨工业大学数学高等研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在量子欧几里得空间上证明了尖锐Hausdorff-Young不等式，并推导出Weyl变换和海森堡群的相应常数，方法基于算子演算和Gabor变换相关的新型算子值流，同时定义了非交换卷积并给出Young不等式的部分结果。
AI中文摘要：
我们在量子欧几里得空间上证明了尖锐的Hausdorff-Young不等式。同时，我们的结果蕴含了Weyl变换以及海森堡群上的尖锐Hausdorff-Young常数。关键要素是一个与Gabor变换相关的新型算子值流。我们的方法主要基于算子演算，因此普遍适用于类似问题。最后，我们给出了非交换卷积的定义，并包含了尖锐Young不等式的部分结果。
英文摘要：
We prove the sharp Hausdorff--Young inequality on the quantum Euclidean space. Our result implies the sharp Hausdorff--Young constants for the Weyl transform, as well as that for Heisenberg groups. The key ingredient is a novel flow related to the mixed-norm of noncommutative Gabor transform. This, meanwhile, implies a new proof of the classical sharp Hausdorff--Young inequality. We then apply the sharp Hausdorff--Young inequality to establish the sharp Young inequality for noncommutative convolution in the range $1\le p,q\le2\le r\le\infty$, with $1/p+1/q=1+1/r$. After appropriate rescaling and trace normalization, this convolution coincides with beam-splitter convolution for bosonic systems, yielding the corresponding Young inequalities with optimal constants in the same range.
