• Corpus ID: 252734849

On Quantum Sobolev Inequalities

@inproceedings{Lafleche2022OnQS,
  title={On Quantum Sobolev Inequalities},
  author={Laurent Lafleche},
  year={2022}
}

• Laurent Lafleche
• Published 6 October 2022
• Mathematics

We investigate the quantum analogue of the classical Sobolev inequalities in the phase space. These inequalities can be seen as a many body uncertainty principle, and also lead to new bounds on the Schatten norms of the Weyl quantization in terms of its symbol. As an intermediate tool, we define a semiclassical analogue of the convolution together with the corresponding Young's and Hardy-Littlewood-Sobolev's inequalities, and introduce quantum Besov spaces. Explicit estimates are obtained on the optimal constants.