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 and logarithmic Sobolev inequalities for the Clifford Dirichlet form,Duke 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.