6 papers
Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincaré Inequalities: a complete characterization of sharp stability and extensions
Anh Xuan Do, Nguyen Lam, Guozhen Lu +1
We introduce a new family of weighted Gaussian -Poincaré-type inequalities with explicit sharp constants, optimizers, and corresponding sharp -gradient stability estimat…
Log-Sobolev and Beckner inequalities and stability of Poincaré inequality with weighted Gaussian measures
Nguyen Lam, Guozhen Lu, Andrey Russanov
We employ a Markov semigroup approach combined with the -calculus to establish a generalized Beckner inequality associated with weighted Gaussian measures. As a direct conseque…
Sharp stability of the Heisenberg Uncertainty Principle: Second-Order and Curl-Free Field Cases
Anh Xuan Do, Nguyen Lam, Guozhen Lu
Using techniques from harmonic analysis, we derive several sharp stability estimates for the second order Heisenberg Uncertainty Principle. We also present the explicit lower and u…
Scale-Dependent Poincaré inequalities, log-Sobolev inequality and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space
Anh Xuan Do, Debdip Ganguly, Nguyen Lam +1
We establish a general scale-dependent Poincaré-Hardy type identity involving a vector field on the hyperbolic space. By choosing suitable parameter, potential and vector field in…
Stability of Gaussian Poincaré inequalities and Heisenberg Uncertainty Principle with monimial weights
Nguyen Lam, Guozhen Lu, Andrey Russanov
We use the Bakry-Ãmery curvature-dimension criterion and -calculus to establish the Poincaré inequality with monomial Gaussian measure, and then apply the duality approach to…
Sobolev interpolation inequalities with optimal Hardy-Rellich inequalities and critical exponents
Nguyen Anh Dao, Anh Xuan Do, Nguyen Lam +1
We establish a new family of the critical higher order Sobolev interpolation inequalities for radial functions as well as for non-radial functions. These Sobolev interpolation ineq…