Generalized Beckner and Poincaré inequalities with stability are established for weighted Gaussian measures, along with log-Sobolev inequalities and applications to the Heisenberg uncertainty principle.
Gross, Hypercontractivity, logarithmic Sobolev inequalities, and applications: a survey of surveys, in Diffusion, Quantum Theory, and Radically Elementary Mathematics, Math
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Log-Sobolev and Beckner inequalities and stability of Poincar\'e inequality with weighted Gaussian measures
Generalized Beckner and Poincaré inequalities with stability are established for weighted Gaussian measures, along with log-Sobolev inequalities and applications to the Heisenberg uncertainty principle.