Sharp upper bound for anisotropic Rényi entropy and Heisenberg uncertainty principle

Key Points

• The study aims to establish the anisotropic Shannon inequality and an uncertainty principle based on Rényi entropy.
• Proved anisotropic Shannon inequality for Rényi entropy on Folland-Stein homogeneous Lie groups.
• Derived the optimal Shannon inequality in the same framework.
• Utilized a logarithmic Sobolev inequality in stratified groups for further proofs.
• Established best constant for anisotropic Shannon inequality.
• Demonstrated optimal Shannon inequality performance.
• Proved Heisenberg-type uncertainty principle in the context of stratified groups.