Article Contents
Article Contents

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

• The uncertainty principle of Heisenberg type can be generalized via the Boltzmann entropy functional. After reviewing the $L^p$ 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 inequalities to show a generalization of uncertainty principle of the Heisenberg type.

Mathematics Subject Classification: Primary: 42B37, 49K20; Secondary: 26D10.

 Citation:

• Figure 1.1.  Young Functions

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