论文标题
关于量子Sobolev不平等
On Quantum Sobolev Inequalities
论文作者
论文摘要
我们研究了相空间中经典Sobolev不等式的量子类似物，其量子Sobolev规范根据换向器的Schatten规范定义。这些不平等为Wigner-Yanase偏斜信息提供了一个不确定性原理，并从其符号方面就Weyl量化的Schatten规范产生了新的界限。作为一种中间工具，我们获得了Hardy-Littlewood-Sobolev的不平等现象的类似物，以进行卷积的半经典类似物，并引入量子空间。在最佳常数上获得了明确的估计。
We investigate the quantum analogue of the classical Sobolev inequalities in the phase space, with the quantum Sobolev norms defined in terms of Schatten norms of commutators. These inequalities provide an uncertainty principle for the Wigner-Yanase skew information, and also lead to new bounds on the Schatten norms of the Weyl quantization in terms of its symbol. As an intermediate tool, we obtain the analogue of Hardy-Littlewood-Sobolev's inequalities for a semiclassical analogue of the convolution, and introduce quantum Besov spaces. Explicit estimates are obtained on the optimal constants.
