Logarithmic Sobolev and Shannon's inequalities and an application to the uncertainty principle

@article{Ogawa2018LogarithmicSA,
  title={Logarithmic Sobolev and Shannon's inequalities and an application to the uncertainty principle},
  author={Takayoshi Ogawa and Kento Seraku},
  journal={Communications on Pure and Applied Analysis},
  year={2018},
  volume={17},
  pages={1651-1669}
}
The uncertainty principle of Heisenberg type can be generalized via the Boltzmann entropy functional. After reviewing the \begin{document} $L^p$ \end{document} generalization of the logarithmic Sobolev inequality by Del Pino-Dolbeault [ 6 ], we introduce a generalized version of Shannon's inequality for the Boltzmann entropy functional which may regarded as a counter part of the logarithmic Sobolev inequality. Obtaining best possible constants of both inequalities, we connect both the… 
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