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.
Wang, Harnack inequalities for log-Sobolev functions and estimates of log-Sobolev constants, Ann
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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.