Sharp upper bound for anisotropic Rényi entropy and Heisenberg uncertainty principle

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Abstract
In this paper, we prove the anisotropic Shannon inequality for the Rényi entropy with the best constant on Folland-Stein homogeneous Lie groups. As a consequence, we also prove the optimal Shannon inequality in the same setting. Using a logarithmic Sobolev inequality in the setting of stratified groups, we prove a Heisenberg-type uncertainty principle in the latter setting.
Funding Information
  • FWO Odysseus 1 (G.0H94.18)
  • Methusalem programme of the Ghent University Special Research Fund (BOF (01M0102)
  • Engineering and Physical Sciences Research Council (EP/R003025/2)
  • Engineering and Physical Sciences Research Council (EP/V005529)
  • Fonds Wetenschappelijk Onderzoek (12B1223N)

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