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Article Dans Une Revue J.Funct.Anal. Année : 2024

On Quantum Sobolev Inequalities

Résumé

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.

Dates et versions

hal-03822983 , version 1 (20-10-2022)

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Citer

Laurent Lafleche. On Quantum Sobolev Inequalities. J.Funct.Anal., 2024, 286 (10), pp.110400. ⟨10.1016/j.jfa.2024.110400⟩. ⟨hal-03822983⟩
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