Demonstrates optimal inequalities for Rényi entropy in homogeneous groups, suggesting foundational implications for entropy studies.
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.
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Chatzakou et al. (2026) studied this question.
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